MultiGraph

Parameters

maxtime : float or None, optional

Specifies the maximum amount of time for core decomposition to spend. The default is None.

inplace : bool, optional

Specifies whether to add the core numbers as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph with core numbers that are stored as a node attribute named core. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

u : numeric or str

Specifies the from node.

v : numeric or str

Specifies the to node.

key : numeric or str

Specifies the key of the edge to add to the graph. The default is None.

Returns

numeric or str

Returns the key of the edge that is added to the graph.

Examples

G.add_edge(1,2,key='A',weight=3,type='parent')

Parameters

edges : an iterable container of edges

Specifies the edges to add to the graph.

Returns

list

Returns the keys of the edges that are added to the graph.

Examples

G.add_edges_from([("A","B",0,{"weight":1,"color":"blue"}),
                     ("C","D",0,{"weight":2,"color":"red"})])

G.add_edges_from([["X","Y",0],["Y","Z",0], weight=1,color= "blue")

Parameters

node : str or number or tuple

Specifies the ID of the node to add to the graph. If the value is a tuple, the first element should contain the node ID, and the second element is a dictionary that represents the node’s attributes.

Parameters

nodes : an iterable container of nodes

Specifies the nodes to add to the graph.

Examples

G.add_nodes_from([('X', {"weight":11,"color": "blue"}), ("Y", {"color": "blue"})])
G.add_nodes_from(('X', 'Y'), weight=1,color= "blue")
G.add_nodes_from(['X', 'Y'])

Parameters

inplace : bool, optional

Specifies whether or not to add the topological order values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a directed graph whose topological order is stored as a node attribute named top_order. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edges : an iterable container of edges

Specifies the weighted edges to add to the graph.

weight : str

Specifies the attribute name for the weighted edges to add. The default is ‘weight’.

Returns

iterator

Returns an iterator over (node, adjacency dictionary) for all nodes in the graph.

Returns

bool

Indicates whether or not the graph allows multiedges.

Returns

bool

Indicates whether or not the graph allows self-loops.

Parameters

node_attr_handler : function or None, optional

Specifies the function to apply to node attributes. The default is None.

edge_attr_handler : function or None, optional

Specifies the function to apply to edge attributes. The default is None.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not to modify the input graph. The default is False.

Returns

SAS graph object or None.

Returns the resulting graph after the function is applied, or returns nothing if the inplace parameter value is True.

Examples

import sasviya.network as sasnet
G = sasnet.Graph([[1,2,{}],[1,3,{'w':1}],[1,4,{'w':2}]])
sasnet.set_node_attributes(G,{1:10,2:20,3:30,4:40},name='x',inplace=True)

#use apply to fillna >>> sasnet.apply(G, edge_attr_handler=lambda data:{‘w’:0 if ‘w’ not in data else data[‘w’]},inplace=True) >>> assert G.edges[(1,2)][‘w’] == 0 >>> print(G.nodes(data=True)) #use apply to negate an attribute >>> sasnet.apply(G, node_attr_handler=lambda data:{‘x’: -data[‘x’]},inplace=True) >>> assert G.nodes[1][‘x’]== -10

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted approximate diameter is computed.

Returns

float

Returns the approximate diameter.

Returns

int

Returns the number of articulation points.

Returns

list

Returns a list of articulation points in the graph.

Parameters

source_direction : {‘in’, ‘out’}

Specifies the degree type (in-degree or out-degree) for the source node in a directed graph.

target_direction : {‘in’, ‘out’}

Specifies the degree type (in-degree or out-degree) for the target node in a directed graph.

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted assortativity degree is computed.

Returns

float

Returns the degree assortativity.

Parameters

node_attr : str

Specifies the name of the nominal node attribute to use.

Returns

float

Returns the nominal assortativity.

Parameters

node_attr : str

Specifies the name of the numeric node attribute to use.

Returns

float

Returns the numeric assortativity.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted average shortest path is computed.

Returns

float

Returns the average shortest path.

Parameters

bins : int or list or str or None, optional

Specifies the bins for the distribution calculation. The default is None. When bins is None, bins are defined as the list of unique component sizes. When bins is int (an integer), it specifies the number of equal-width bins. When bins is a list, it specifies bin ranges and should be monotonically increasing. For example, a value of [a1, a2, a3, a4] results in the following bin ranges: [a1, a2) (inclusive of a1 but exclusive of a2), [a2, a3), and [a3, a4]. When bins is str (a string), it specifies the method to use for calculating the bin ranges. For example, ‘stone’,’auto’,’doane’,’fd’,’rice’,’scott’,’sqrt’,’sturges’. See https://numpy.org/doc/stable/reference/generated/numpy.histogram.html for more information about the bins parameter.

Returns

dict

Returns a dictionary where the key is the bin’s lower-bound value and the value is the number of biconnected components whose edge count is within the range of the bin.

Parameters

bins : int or list or str or None, optional

Specifies the bins for the distribution calculation. The default is None. When bins is None, bins are defined as the list of unique component sizes. When bins is int (an integer), it specifies the number of equal-width bins. When bins is a list, it specifies bin ranges and should be monotonically increasing. For example, a value of [a1, a2, a3, a4] results in the following bin ranges: [a1, a2) (inclusive of a1 but exclusive of a2), [a2, a3), and [a3, a4]. When bins is str (a string), it specifies the method to use for calculating the bin ranges. For example, ‘stone’,’auto’,’doane’,’fd’,’rice’,’scott’,’sqrt’,’sturges’. See https://numpy.org/doc/stable/reference/generated/numpy.histogram.html for more information about the bins parameter.

Returns

dict

Returns a dictionary where the key is the bin’s lower-bound value and the value is the number of biconnected components whose node count is within the range of the bin.

Returns

dict

Returns a dictionary in which the keys are biconnected component IDs and the values are the number of edges within each component.

Returns

dict

Returns a dictionary in which the keys are biconnected component IDs and the values are the number of nodes within each component.

Returns

int

Returns the number of biconnected components.

Parameters

order_by : ‘node’ or ‘edge’ or None, optional

Specifies the parameter that is used to sort the components by the number of nodes or edges within each component. The default is None, which means that the components are not sorted.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

ascending : bool, optional

Specifies whether to sort in ascending or descending order, when you specify the order_by parameter. The default is False.

Yields

generator

Returns the result as a generator of biconnected component subgraphs. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

return_nodes_map : bool, optional

Specifies whether or not to also compute the block-cut tree node map. The default is False.

Returns

SAS graph object

Returns a graph that represents the block-cut tree. When return_nodes_map = True, the output graph has the nodes_map attribute, which contains a dictionary that maps its nodes to a list of nodes in the original graph. Note: If a block is empty (that is, the corresponding biconnected component contains only articulation points), that block does not appear as a key in the nodes_map dictionary.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that unweighted betweenness centrality is computed.

sample_percent : int, optional

Specifies the percentage of source nodes to sample for the approximate betweenness calculation. This parameter value should be in the range (0, 100]. The default is 100.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the node and edge attributes between_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted closeness centrality is computed.

nopath : {‘diameter’, ‘harmonic’, or ‘zero’}, optional

Specifies a method to use for accounting for the shortest path distance between two nodes when a path does not exist. The valid values are as follows: - ‘diameter’ uses the graph diameter (plus one) as the shortest path distance between disconnected nodes. - ‘harmonic’ uses the harmonic formula for calculating closeness centrality. - ‘zero’ uses zero as the shortest path distance between disconnected nodes.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the closeness centrality node attributes centr_close_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted degree centrality is computed.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the degree centrality node attributes centr_degree_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted eigenvector centrality is computed.

maxiters : int, optional

Specifies the maximum number of iterations in order to limit the amount of computation time that is spent when convergence is slow. The default is 10,000.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the degree centrality node attributes centr_eigen_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted hub and authority centrality is computed.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the hub and authority centrality node attributes centr_hub_* and centr_auth_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted influence centrality is computed.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the first- and second-order influence centrality node attributes centr_influence1_* and centr_influence2_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that unweighted PageRank centrality is computed.

alpha : float, optional

Specifies the damping parameter for the PageRank centrality (or algorithm). The default is 0.85.

tolerance : float, optional

Specifies the tolerance parameter for the PageRank centrality (or algorithm). The default is 1E-9.

inplace : bool, optional

Specifies whether to add the centrality values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that contains the PageRank centrality node attributes centr_pagerank_*. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

bins : int or list or str, optional

Specifies the bins for the distribution calculation. The default is None. When bins is None, bins are defined as the list of unique component sizes. When bins is an integer (int), it represents the number of equal-width bins. When bins is a list, it specifies bin ranges and it should be monotonically increasing. For example, a value of [a1, a2, a3, a4] results in the following bin ranges: [a1, a2) (inclusive of a1 but exclusive of a2), [a2, a3), and [a3, a4]. When bins is a string (str), it specifies the method to be used for calculating the bin ranges. For example, ‘stone’, ‘auto’, ‘doane’, ‘fd’, ‘rice’, ‘scott’, ‘sqrt’, ‘sturges’. See https://numpy.org/doc/stable/reference/generated/numpy.histogram.html for more information about the bins parameter.

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

Returns

dict

Returns a dictionary where the key is the bin’s lower-bound value and the value is the number of components whose edge count within the range of the bin.

Parameters

bins : int or list or str or None, optional

Specifies the bins for the distribution calculation. The default is None. When bins is None, bins are defined as the list of unique component sizes. When bins is an integer (int), it represents the number of equal-width bins. When bins is a list, it specifies bin ranges and it should be monotonically increasing. For example, a value of [a1, a2, a3, a4] results in the following bin ranges: [a1, a2) (inclusive of a1 but exclusive of a2), [a2, a3), and [a3, a4]. When bins is a string (str), it specifies the method to use for calculating the bin ranges. For example, ‘stone’, ‘auto’, ‘doane’, ‘fd’, ‘rice’, ‘scott’, ‘sqrt’, ‘sturges’. See https://numpy.org/doc/stable/reference/generated/numpy.histogram.html for more information about the bins parameter.

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

Returns

dict

Returns a dictionary where the key is the bin’s lower-bound value and the value is the number of components whose node count is within the range of the bin.

Parameters

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

Returns

dict

Returns a dictionary in which the keys are connected component IDs and the values are the number of edges within each component.

Parameters

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

Returns

dict

Returns a dictionary in which the keys are connected component IDs and the values are the number of nodes within each component.

Returns

int

Returns the number of connected components.

Parameters

order_by : ‘node’ or ‘edge’ or None, optional

Specifies whether to sort the components by the number of nodes or edges within each component. The default is None, which means that the components are not sorted.

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

ascending : bool, optional

Specifies whether to sort in ascending or descending order, when you specify the order_by parameter. The default is False.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one connected component. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, meaning that the node and edge attributes of the graph are retained.

Returns

SAS graph object

Returns an independent copy of the input.

Parameters

maxtime : float or None, optional

Specifies the maximum amount of time for core decomposition to spend. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one k-core in increasing core number. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

maxcycles : int or ‘ALL’, optional

Specifies the maximum number of cycles to count. The default is ‘ALL’.

minlength : int, optional

Specifies the minimum number of edges in cycles that are counted. The default is 1.

maxlength : int, optional

Specifies the maximum number of edges in cycles that are counted. The default is None.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None. When the value is None, a weight of 1 is assumed for all nodes.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None. When the value is None, a weight of 1 is assumed for all edges.

minedgewt : float or None, optional

Specifies the minimum sum of edge weights in a cycle. The default is None.

maxedgewt : float or None, optional

Specifies the maximum sum of edge weights in a cycle. The default is None.

minnodewt : float or None, optional

Specifies the minimum sum of node weights in a cycle. The default is None.

maxnodewt : float or None, optional

Specifies the maximum sum of node weights in a cycle. The default is None.

maxtime : float or None, optional

Specifies the approximate maximum number of seconds to spend on enumeration. The default is None.

source : node or None, optional

Specifies the source node for cycle calculations. The default is None.

Returns

int

Returns a count of cycles in the graph.

Parameters

n : single node or container of nodes or None, optional

Specifies which nodes to include. The default is None, which means that the degree of every node is returned.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None.

Returns

int or dictionary

Returns the degree of specified node(s).

Returns

float

Returns the density of the graph.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted diameter is computed.

Returns

int or float

Returns the diameter.

Parameters

attributes_subset : str or list, optional

Specifies the edge attribute or a list of the edge attributes to remove; for example, ‘weight’ or [‘weight’,’color’]. By default, all edge attributes are removed.

edges_subset : list or iterable of edges, optional

Specifies the edges to remove attributes from; for example, [(1,2),(2,3)]. By default the attributes for all edges are removed.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

Returns

SAS graph object or None

If the inplace parameter value is True, the graph is modified by removing the specified edge attributes. If the inplace parameter value is False, a copy of the input graph with the modified edge attributes is returned.

Parameters

attributes_subset : str or list, optional

Specifies the node attribute or list of node attributes to remove; for example, [‘weight’,’color’]. By default, all node attributes are removed.

nodes_subset : list or iterable of nodes, optional

Specifies the nodes to drop attributes from; for example, [1,2,3] or (1,2,3) or [1] or (1,). By default, the attributes for all nodes are removed.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

Returns

SAS graph object or None

If the inplace parameter value is True, the graph is modified by removing the specified node attributes. If the inplace parameter value is False, a copy of the input graph with the modified node attributes is returned.

Parameters

maxcycles : int or ‘ALL’, optional

Specifies the maximum number of cycles to count. The default is ‘ALL’.

minlength : int, optional

Specifies the minimum number of edges in cycles that are counted. The default is 1.

maxlength : int, optional

Specifies the maximum number of edges in cycles that are counted. The default is None.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None. When the value is None, a weight of 1 is assumed for all nodes.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None. When the value is None, a weight of 1 is assumed for all edges.

minedgewt : float or None, optional

Specifies the minimum sum of edge weights in a cycle. The default is None.

maxedgewt : float or None, optional

Specifies the maximum sum of edge weights in a cycle. The default is None.

minnodewt : float or None, optional

Specifies the minimum sum of node weights in a cycle. The default is None.

maxnodewt : float or None, optional

Specifies the maximum sum of node weights in a cycle. The default is None.

maxtime : float or None, optional

Specifies the approximate maximum number of seconds to spend on enumeration. The default is None.

source : node or None, optional

Specifies the source node for cycle calculations. The default is None.

Yields

generator

Yields a generator of cycles, each of which is given as a list of the cycles’ edges. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

maxcycles : int or ‘ALL’, optional

Specifies the maximum number of cycles to count. The default is ‘ALL’.

minlength : int, optional

Specifies the minimum number of edges in cycles that are counted. The default is 1.

maxlength : int, optional

Specifies the maximum number of edges in cycles that are counted. The default is None.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None. When the value is None, a weight of 1 is assumed for all nodes.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None. When the value is None, a weight of 1 is assumed for all edges.

minedgewt : float or None, optional

Specifies the minimum sum of edge weights in a cycle. The default is None.

maxedgewt : float or None, optional

Specifies the maximum sum of edge weights in a cycle. The default is None.

minnodewt : float or None, optional

Specifies the minimum sum of node weights in a cycle. The default is None.

maxnodewt : float or None, optional

Specifies the maximum sum of node weights in a cycle. The default is None.

maxtime : float or None, optional

Specifies the approximate maximum number of seconds to spend on enumeration. The default is None.

source : node or None, optional

Specifies the source node for cycle calculations. The default is None.

Yields

generator

Yields a generator of cycles, each of which is given as a list of the cycles’ nodes. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

maxcycles : int or ‘ALL’, optional

Specifies the maximum number of cycles to count. The default is ‘ALL’.

minlength : int, optional

Specifies the minimum number of edges in cycles that are counted. The default is 1.

maxlength : int, optional

Specifies the maximum number of edges in cycles that are counted. The default is None.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None. When the value is None, a weight of 1 is assumed for all nodes.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None. When the value is None, a weight of 1 is assumed for all edges.

minedgewt : float or None, optional

Specifies the minimum sum of edge weights in a cycle. The default is None.

maxedgewt : float or None, optional

Specifies the maximum sum of edge weights in a cycle. The default is None.

minnodewt : float or None, optional

Specifies the minimum sum of node weights in a cycle. The default is None.

maxnodewt : float or None, optional

Specifies the maximum sum of node weights in a cycle. The default is None.

maxtime : float or None, optional

Specifies the approximate maximum number of seconds to spend on enumeration. The default is None.

source : node or None, optional

Specifies the source node for cycle calculations. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one cycle of the same type as the input graph. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

minlength : int, optional

Specifies the minimum number of edges in paths that are returned. The default is 1.

maxlength : int or None, optional

Specifies the maximum number of edges in paths that are returned. The default is None.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None, which means that a weight of 1 is assumed for all nodes.

minedgewt : float or None, optional

Specifies the minimum edge weight of edges in paths that are returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum edge weight of edges in paths that are returned. The default is None.

minnodewt : float or None, optional

Specifies the minimum node weight of nodes in paths that are returned. The default is None.

maxnodewt : float or None, optional

Specifies the maximum node weight of nodes in paths that are returned. The default is None.

maxtime : float or None, optional

Specifies the maximum amount of time for enumeration to spend. The default is None.

Yields

generator

Yields a generator of Path objects, each of which is given as a list of the paths’ edges. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

minlength : int, optional

Specifies the minimum number of edges in paths that are returned. The default is 1.

maxlength : int or None, optional

Specifies the maximum number of edges in paths that are returned. The default is None.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None, which means that a weight of 1 is assumed for all nodes.

minedgewt : float or None, optional

Specifies the minimum edge weight of edges in paths that are returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum edge weight of edges in paths that are returned. The default is None.

minnodewt : float or None, optional

Specifies the minimum node weight of nodes in paths that are returned. The default is None.

maxnodewt : float or None, optional

Specifies the maximum node weight of nodes in paths that are returned. The default is None.

maxtime : float or None, optional

Specifies the maximum amount of time for enumeration to spend. The default is None.

Yields

generator

Yields a generator of Path objects, each of which is given as a list of the paths’ nodes. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

minlength : int, optional

Specifies the minimum number of edges in paths that are returned. The default is 1.

maxlength : int or None, optional

Specifies the maximum number of edges in paths that are returned. The default is None.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None, which means that a weight of 1 is assumed for all nodes.

minedgewt : float or None, optional

Specifies the minimum edge weight of edges in paths that are returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum edge weight of edges in paths that are returned. The default is None.

minnodewt : float or None, optional

Specifies the minimum node weight of nodes in paths that are returned. The default is None.

maxnodewt : float or None, optional

Specifies the maximum node weight of nodes in paths that are returned. The default is None.

maxtime : float or None, optional

Specifies the maximum amount of time for enumeration to spend. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one Path object. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

sequence : iterable of nodes

Specifies the order in which to visit the required nodes.

pathsperpair : int, optional

Specifies the maximum number of shortest paths to return. The default is 1.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted shortest path is computed.

minedgewt : float or None, optional

Specifies the minimum total edge weight for each shortest path that is returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum total edge weight for each shortest path that is returned. The default is None.

maxabsobjgap : nonnegative float or None, optional

Specifies the maximum weight by which a returned path can exceed the optimum shortest path weight. The default is None.

maxrelobjgap : nonnegative float or None, optional

Specifies the maximum factor by which a returned path can exceed the optimum shortest path weight. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of Path objects; each object represents a subpath between a sequence of nodes. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

pathsperpair : int, optional

Specifies the maximum number of shortest paths to return for each source-sink pair. The default is 1.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted shortest path is computed.

minedgewt : float or None, optional

Specifies the minimum total edge weight for each shortest path that is returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum total edge weight for each shortest path that is returned. The default is None.

maxabsobjgap : nonnegative float or None, optional

Specifies the maximum weight by which a returned path can exceed the optimum shortest path weight. The default is None.

maxrelobjgap : nonnegative float or None, optional

Specifies the maximum factor by which a returned path can exceed the optimum shortest path weight. The default is None.

Yields

generator

Yields a generator of paths; each path is given as a list of the paths’ edges. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

pathsperpair : int, optional

Specifies the maximum number of shortest paths to return for each source-sink pair. The default is 1.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted shortest path is computed.

minedgewt : float or None, optional

Specifies the minimum total edge weight for each shortest path that is returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum total edge weight for each shortest path that is returned. The default is None.

maxabsobjgap : nonnegative float or None, optional

Specifies the maximum weight by which a returned path can exceed the optimum shortest path weight. The default is None.

maxrelobjgap : nonnegative float or None, optional

Specifies the maximum factor by which a returned path can exceed the optimum shortest path weight. The default is None.

Yields

generator

Yields a generator of paths; each path is given as a list of the paths’ nodes. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as source nodes.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) for shortest path enumeration. The default is None, which means that all nodes within the graph are used as sink nodes.

pathsperpair : int, optional

Specifies the maximum number of shortest paths to return for each source-sink pair. The default is 1.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted shortest path is computed.

minedgewt : float or None, optional

Specifies the minimum total edge weight for each shortest path that is returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum total edge weight for each shortest path that is returned. The default is None.

maxabsobjgap : nonnegative float or None, optional

Specifies the maximum weight by which a returned path can exceed the optimum shortest path weight. The default is None.

maxrelobjgap : nonnegative float or None, optional

Specifies the maximum factor by which a returned path can exceed the optimum shortest path weight. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of Path objects; each object represents one shortest path. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

node_type : str

Specifies the node attribute to consider in constructing the metagraph.

edge_type : str, optional

Specifies the edge attribute to consider in constructing the metagraph. By default, all connections between nodes are considered the same.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

Returns

SAS graph object

Returns the metagraph, which has an edge attribute count and determines the number of unique connections between pairs of nodes.

Parameters

n : int

Specifies the number of graphs to return.

order_by : ‘node’ or ‘edge’ or None

Specifies whether to sort the biconnected components by the number of nodes or edges within those components. The default is None, which means that the biconnected components are not sorted.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

ascending : bool

Specifies whether to sort in ascending or descending order, when you specify the order_by parameter. When the value is True, the smallest biconnected components are returned instead. The default is False.

Returns

list

Returns a list of n largest or smallest biconnected components of a graph.

Parameters

n : int

Specifies the number of graphs to return.

order_by : ‘node’ or ‘edge’

Specifies whether to sort the component by number of nodes or edges within that component. The default is None, which means that the result is not sorted.

strongly : bool, optional

Specifies whether or not the connected components must be strongly connected. When the value is False, only weakly connected components are found. This parameter is supported only for directed graphs. The default is True.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

ascending : bool, optional

Specifies whether to sort in ascending or descending order, when you specify the order_by parameter. The default is False.

Returns

list

Returns a list of the n largest connected components of a graph.

Parameters

name : str

Specifies the name of the edge attribute.

all_edges : bool, optional

Specifies whether or not to check for the existence of the edge attribute in all or any of the edges. The default is False.

Returns

bool

If the all_edges parameter value is True, the value True is returned if that edge attribute exists in all edges; otherwise the value False is returned. If the all_edges parameter value is False, the value True is returned if at least one edge in the graph has that specified edge attribute.

Parameters

name : str

Specifies the name of the node attribute.

all_nodes : bool, optional

Specifies whether or not to check for the existence of the node attribute in all or any of the nodes. The default is False.

Returns

bool

If the all_nodes parameter value is True, the value True is returned if that node attribute exists in all node; otherwise the value False is returned. If the all_nodes parameter value is False, the value True is returned if at least one node in the graph has that specified node attribute.

Parameters

rhs : SAS graph object

Specifies the other graph, of the same type as self, with which to intersect.

nodes_attrs_agg : function or str or dict or None, optional

Specifies how to aggregate node attributes. The value can be a function, such as mean or np.sum; a string in the list {‘first’,’last’,’mean’}; or a dictionary that maps node attributes to functions. The default is None.

edges_attrs_agg : function or str or dict or None, optional

Specifies how to aggregate edge attributes. The value can be a function, such as mean or np.sum; a string in the list {‘first’,’last’,’mean’}; or a dictionary that maps edge attributes to functions. The default is None.

Returns

SAS graph object

Returns a graph that is constructed by the intersection of the two graphs.

Returns

bool

Indicates whether the input graph is biconnected (True) or not (False).

Returns

bool

Indicates whether the input graph is bipartite.

Returns

bool

Indicates whether the input graph is connected (True) or not (False).

Returns

bool

Indicates whether the input graph is a simple cycle (True) or not (False).

Returns

bool

Indicates whether the input graph is a directed acyclic graph (DAG).

Returns

bool

Indicates whether or not the graph is directed.

Parameters

maxtime : float or None, optional

Specifies the maximum amount of time to determine whether or not the graph is Hamiltonian. The default is None.

Returns

bool or None

Indicates whether or not the input graph is determined to be Hamiltonian. Returns None if no determination is made.

Returns

bool

Indicates whether or not the graph is immutable.

Returns

bool

Indicates whether or not the graph allows multiedges.

Returns

bool

Indicates whether the input graph is a simple path (True) or not (False).

Returns

bool

Indicates whether the input graph is strongly connected (True) or not (False).

Returns

bool

Indicates whether the input graph is weakly connected (True) or not (False).

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

maxiters : int, optional

Specifies the number of iterations that the algorithm can run. The default is 100.

tolerance : float, optional

Specifies the value for which the algorithm stops iterating when the fraction of label changes for all nodes in the graph is less than the value. The default is 0.05.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one community. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

maxiters : int, optional

Specifies the number of iterations that the algorithm can run. The default is 100.

tolerance : float, optional

Specifies the value for which the algorithm stops iterating when the fraction of label changes for all nodes in the graph is less than the value. The default is 0.05.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

inplace : bool, optional

Specifies whether to add the community values as attributes to the input graph directly or to create a copy of the graph. The default is False.

Returns

SAS graph object or None

Returns a graph that contains the node attribute community, which denotes the community assignment for each node. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Returns

int

Returns the number of leaf nodes.

Parameters

inplace : bool, optional

Specifies whether to add the transitivity values as attributes to the input graph directly or to create a copy of the graph. The default is False.

Returns

SAS graph object or None

Returns a graph that contains node attribute ‘transitivity’. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

resolution : float, optional

Specifies the factor in the modularity equation that affects the expected number of links between two nodes. A higher value produces more communities. The default is 1.

tolerance : float, optional

Specifies the value for which the algorithm stops iterating when the fraction of modularity gain between two consecutive iterations is less than the value. The default is 0.001.

maxiters : int, optional

Specifies the number of iterations that the algorithm can run. The default is 100.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one community. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

resolution : float, optional

Specifies the factor in the modularity equation that affects the expected number of links between two nodes. A higher value produces more communities. The default is 1.

tolerance : float, optional

Specifies the value for which the algorithm stops iterating when the fraction of modularity gain between two consecutive iterations is less than the value. The default is 0.001.

maxiters : int, optional

Specifies the number of iterations that the algorithm can run. The default is 100.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

inplace : bool, optional

Specifies whether to add the community values as attributes to the input graph directly or to create a copy of the graph. The default is False.

Returns

SAS graph object or None

Returns a graph that contains the node attribute community, which denotes the community assignment for each node. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : number or str

Specifies the source node for the maximum flow.

sink : number or str

Specifies the sink node for the maximum flow.

capacity_attr : str, optional

Specifies the name of the edge attribute that contains the capacity of the edge. The default is ‘upper’.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the edge attribute flow, which contains the flow values. This graph has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is True, the graph is modified in place and None is returned. When the inplace parameter value is False, the returned graph contains only the flow edges.

Parameters

maxcliques : int or ‘ALL’, optional

Specifies the maximum number of enumerated cliques to return. The default is ‘ALL’.

node_weight : str or None, optional

Specifies the node attribute that corresponds to the node weight. The default is None, which means that a weight of 1 is assumed for all nodes.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

minsize : int, optional

Specifies the minimum number of nodes in a clique. The default is 1.

maxsize : int or None, optional

Specifies the maximum number of nodes in a clique. The default is None.

minedgewt : float or None, optional

Specifies the minimum sum of edge weights in a clique. The default is None.

maxedgewt : float or None, optional

Specifies the maximum sum of edge weights in a clique. The default is None.

minnodewt : float or None, optional

Specifies the minimum sum of node weights in a clique. The default is None.

maxnodewt : float or None, optional

Specifies the maximum sum of node weights in a clique. The default is None.

maxtime : float or None, optional

Specifies the approximate maximum number of seconds for enumeration to spend. The default is None.

order_by : ‘node’ or None, optional

Specifies whether to sort the cliques by the number of nodes within each clique. The default is None, which means that the result is not sorted.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

ascending : bool, optional

Specifies whether to sort in ascending or descending order, when you specify the order_by parameter. The default is False.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one maximal clique. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that an unweighted minimum cut is calculated.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the edge attribute ‘mincut’, which indicates the edges to include in the minimum cut set, and the node attribute ‘mincut_partition’, which indicates the node partition of the calculated minimum cut. This graph has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is True, the graph is modified in place and None is returned. When the inplace parameter value is False, a modified copy of the graph is returned.

Parameters

source : number or str

Specifies the source node (s) for the minimum s-t cut.

sink : number or str

Specifies the sink node (t) for the minimum s-t cut.

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that an unweighted minimum s-t cut is calculated.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the edge attribute s_t_cut, which indicates the edges to include in the minimum s-t cut set; and the node attribute s_t_cut_partition, which indicates the node partition of the calculated minimum s-t cut. This graph has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is True, the graph is modified in place and None is returned. When the inplace parameter value is False, a modified copy of the graph is returned.

Parameters

demand_lower_attr : str, optional

Specifies the name of the node attribute that contains the lower bound of the node supply. The default is ‘lower’.

demand_upper_attr : str, optional

Specifies the name of the node attribute that contains the upper bound of the node supply. The default is ‘upper’.

capacity_lower_attr : str, optional

Specifies the name of the edge attribute that contains the capacity lower bound of the edge. The default is ‘lower’.

capacity_upper_attr : str, optional

Specifies the name of the edge attribute that contains the capacity upper bound of the edge. The default is ‘upper’.

cost_attr : str, optional

Specifies the name of the edge attribute that contains the edge cost. The default is ‘weight’.

maxtime : float or None, optional

Specifies the maximum amount of time to allow for computing the minimum-cost network flow. The default is None.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the edge attributes flow and reduced_cost, which contain the flow and reduced cost values, respectively; and the node attribute dual, which contains the optimal dual value. This graph has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is True, the graph is modified in place and None is returned.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

source : number or str or None

Specifies the source node for a directed MST. The default is None.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the edge attribute ‘mst’, which indicates the edges to include in the spanning tree or forest. This graph has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is True, the graph is modified in place and None is returned. When the inplace parameter value is False, the returned graph contains only the spanning tree or forest edges.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Returns

SAS graph object

Returns a directed graph whose edges identify the assignment mapping in the minimum-weight full matching solution. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

n : node

Specifies a node in the graph.

Returns

iterator

Returns an iterator over all neighbors of node n.

Parameters

u : numeric or str

Specifies the from node to add to the graph.

v : numeric or str

Specifies the to node to add to the graph.

Returns

int

Returns a unique edge key value.

Parameters

inplace : bool, optional

Specifies whether to add the clique number values as attributes to the input graph directly or to create a copy of the graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the value of the inplace parameter is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph or modifies the existing graph to contain the node attribute clique_number, which includes the clique number of each node. The graph g has the attribute g.solution_summary, which contains information about the results of the algorithm.

Parameters

u : numeric or str or None, optional

Specifies the from node. The default is None.

v : numeric or str or None, optional

Specifies the to node. The default is None.

Returns

int

Returns the number of edges in the graph. When you specify u and v, the number of edges between u and v is returned. When you specify u but v is None, the number of edges that connect to u is returned. When you specify v but u is None, the number of edges that connect to v is returned.

Returns

int

Returns the number of nodes in the graph.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in self other than nodes.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the converging method is used. When the directed_method parameter is specified for an undirected graph, a ValueError is raised.

multigraph : bool, optional

Specifies whether or not to return a multigraph. When the value is True, the algorithm returns a multigraph in which the multiple edges represent multiple shared neighbors. The edge attribute ‘neighbor’ stores the label of the shared neighbor. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the neighbors subset of nodes. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in g other than nodes.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the converging method is used.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the neighbors subset of nodes. The strength of association in the calculated projection is represented by the ‘adamic_adar’ edge attribute.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in g other than those that are specified by the nodes parameter.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the converging method is used.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the neighbors subset of nodes. The strength of association in the calculated projection is represented by the ‘common_neighbors’ edge attribute.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in g other than those that are specified by the nodes parameter.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the ‘converging’ method is used.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the neighbors subset of nodes. The strength of association in the calculated projection is represented by the ‘cosine’ edge attribute.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in g other than those that are specified by the nodes parameter.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the ‘converging’ method is used.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the subset of nodes that are specified by the neighbors parameter. The strength of association in the calculated projection is represented by the ‘dice’ edge attribute.

Parameters

nodes : list or iterable

Specifies the subset of nodes to project onto.

neighbors : list or iterable, optional

Specifies the subset of nodes to project through. By default, this subset consists of all nodes in g other than those that are specified by the nodes parameter.

directed_method : {‘converging’, ‘diverging’, ‘transitive’}, optional

Specifies a method to use for projecting directed graphs. By default, the ‘converging’ method is used.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained.

Returns

SAS graph object

Returns a graph representation of the node pairs with common neighbors among the neighbors subset of nodes. The strength of association in the calculated projection is represented by the ‘jaccard’ edge attribute.

Parameters

q : graph

Specifies the query graph.

expr : _Expression or None, optional

Specifies additional logic to filter the query results. The default is None.

induced : bool, optional

Specifies whether or not to return only node-induced matches. The default is False.

break_symmetry : bool, optional

Specifies whether or not to break symmetry and eliminate automorphic relationships between matches. The default is False.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one isomorphic mapping from q to self. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to compute the reach network.

max_reach : int, optional

Specifies the number of steps (or hops) to traverse from the source nodes. The default is 1.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Returns

SAS graph object

Returns a graph that represents the reach network. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to compute the reach network.

max_reach : int, optional

Specifies the number of steps (or hops) to traverse from the source nodes. The default is 1.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of subgraphs; each subgraph represents one reach network. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

u : numeric or str

Specifies the from node.

v : numeric or str

Specifies the to node.

key : numeric or str or None

Specifies the edge key. The default is None, which means that when there are multiple edges between u and v, the most recently added edge is removed.

Examples

G.remove_edge(1,2)

Parameters

edges : an iterable container of edges

When you specify two-tuples (u, v), the most recently added edge between u and v is removed. When you specify three-tuples (u, v, key) or four-tuples (u, v, key, data), the edge between u and v with the specified key is removed, where data are ignored.

Parameters

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not to modify the input graph. The default is False.

Returns

SAS graph object or None

Returns the resulting graph after isolated nodes are removed, or returns nothing if the inplace parameter value is True.

Parameters

node : numeric or str

Specifies the node to remove from the graph.

Parameters

nodes : an iterable container of nodes

Specifies the nodes to remove from the graph.

Parameters

values : scalar or dict-like or Pandas DataFrame

Specifies what the edge attribute should be set to. When this parameter is set to a Pandas DataFrame, it is expected to have from, to, and edge_key (only for multigraphs) columns, and the other columns are treated as edge attributes to add. When values is a dictionary, the keys are edges and the values are either edge attribute values or dictionaries of attribute name-value pairs. For multigraphs, the edge tuples must be of the form (u, v, key). For simple graphs, the keys must be tuples of the form (u, v). When this parameter is not set to a dictionary, it is treated as a single attribute value that is then applied to every edge in self. The attribute name is specified by the name parameter.

name : str or None, optional

Specifies the name of the edge attribute to set if the values parameter is set to a scalar. The default is None.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not to modify the graph in place. The default is False.

Returns

SAS graph object or None

If the inplace parameter value is False, a copy of the input graph with the new edge attributes is returned. If the inplace parameter value is True, the graph is modified by setting the specified edge attributes.

Parameters

values : scalar or dict-like or Pandas DataFrame

Specifies what the node attribute should be set to. When values is not a dictionary, it is treated as a single attribute value that is then applied to every node in self. This means that if you provide a mutable object, such as a list, updates to that object are reflected in the node attribute for every node. The attribute name is specified by the name parameter. When values is a dictionary, the keys are nodes and the values are either node attribute values or dictionaries of attribute name-value pairs.

name : str or None, optional

Specifies the name of the node attribute to set if the values parameter is set to a scalar. The default is None.

immutable : bool or None, optional

Specifies whether or not to return an immutable copy. The default is None, which means that the mutability matches the input graph.

inplace : bool, optional

Specifies whether or not the graph is modified in place. The default is False.

Returns

SAS graph object or None

If the inplace parameter value is True, the graph is modified by setting the specified node attributes. If the inplace parameter value is False, a copy of the input graph with the new node attributes is returned.

Parameters

source : node or iterable of nodes or None, optional

Specifies the source node(s) and restricts enumeration to the shortest paths that contain the specified source node(s). The default is None.

sink : node or iterable of nodes or None, optional

Specifies the sink node(s) and restricts enumeration to the shortest paths that contain the specified sink node(s). The default is None.

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that the unweighted shortest path is computed.

minedgewt : float or None, optional

Specifies the minimum total edge weight for each shortest path that is returned. The default is None.

maxedgewt : float or None, optional

Specifies the maximum total edge weight for each shortest path that is returned. The default is None.

Returns

dict

Returns a dictionary where each key is a (source, sink) tuple and its value is the corresponding shortest source-sink path distance.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to calculate similarity.

sink : node or iterable of nodes, optional

Specifies one or more source nodes from which to calculate similarity. By default, all nodes are sinks.

top_k : int, optional

Specifies the maximum number of highest-similarity source-sink pairs to return.

bottom_k : int, optional

Specifies the maximum number of lowest-similarity source-sink pairs to return.

exclude_source : bool, optional

Specifies whether or not to exclude the source-source pairs from the returned results. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned results. The default is False.

Returns

OrderedDict

Returns an ordered dictionary, sorted in decreasing order of similarity. The key is the (source, sink) tuple, and the value is the computed similarity score.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to calculate similarity.

sink : node or iterable of nodes, optional

Specifies one or more source nodes from which to calculate similarity. By default, all nodes are sinks.

top_k : int, optional

Specifies the maximum number of highest-similarity source-sink pairs to return.

bottom_k : int, optional

Specifies the maximum number of lowest-similarity source-sink pairs to return.

exclude_source : bool, optional

Specifies whether or not to exclude the source-source pairs from the returned results. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned results. The default is False.

Returns

OrderedDict

Returns an ordered dictionary, sorted in decreasing order of similarity. The key is the (source, sink) tuple, and the value is the computed similarity score.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to calculate similarity.

sink : node or iterable of nodes, optional

Specifies one or more source nodes from which to calculate similarity. By default, all nodes are sinks.

top_k : int, optional

Specifies the maximum number of highest-similarity source-sink pairs to return.

bottom_k : int, optional

Specifies the maximum number of lowest-similarity source-sink pairs to return.

exclude_source : bool, optional

Specifies whether or not to exclude the source-source pairs from the returned results. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned results. The default is False.

Returns

OrderedDict

Returns an ordered dictionary, sorted in decreasing order of similarity. The key is the (source, sink) tuple, and the value is the computed similarity score.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to calculate similarity.

sink : node or iterable of nodes, optional

Specifies one or more source nodes from which to calculate similarity. By default, all nodes are sinks.

top_k : int, optional

Specifies the maximum number of highest-similarity source-sink pairs to return.

bottom_k : int, optional

Specifies the maximum number of lowest-similarity source-sink pairs to return.

exclude_source : bool, optional

Specifies whether or not to exclude the source-source pairs from the returned results. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned results. The default is False.

Returns

OrderedDict

Returns an ordered dictionary, sorted in decreasing order of similarity. The key is the (source, sink) tuple, and the value is the computed similarity score.

Parameters

measure : str, one of {‘adamic_adar’, ‘common_neighbors’, ‘cosine’, ‘dice’, ‘jaccard’}

Specifies the metric to be used to compute the node similarity.

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the edge attribute that corresponds to the measure name. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the ‘adamic_adar’ edge attribute. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the ‘common_neighbors’ edge attribute. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

edge_weight : str or None, optional

Specifies the edge attribute that corresponds to the edge weight. The default is None, which means that a weight of 1 is assumed for all edges.

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the ‘cosine’ edge attribute. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the dice edge attribute. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

min_score : float, optional

Specifies the minimum similarity score for edges in the output graph. The default is sys.float_info.epsilon.

max_score : float, optional

Specifies the maximum similarity score for edges in the output graph. The default is np.inf.

exclude_source : bool, optional

Specifies whether or not to exclude self-loops from the returned graph. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned graph. The default is False.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node attributes of the graph are retained. Note that the edge attributes are not carried over to the output graph.

Returns

MultiGraph

Returns a MultiGraph representation of the node pairs whose similarity scores are in the range of min_score to max_score. The calculated similarity is represented by the ‘jaccard’ edge attribute. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

source : node or iterable of nodes

Specifies one or more source nodes from which to calculate similarity.

sink : node or iterable of nodes, optional

Specifies one or more source nodes from which to calculate similarity. By default, all nodes are sinks.

top_k : int, optional

Specifies the maximum number of highest-similarity source-sink pairs to return.

bottom_k : int, optional

Specifies the maximum number of lowest-similarity source-sink pairs to return.

exclude_source : bool, optional

Specifies whether or not to exclude the source-source pairs from the returned results. The default is False.

exclude_existing_neighbors : bool, optional

Specifies whether or not to exclude source-sink pairs that are joined by an existing link from the returned results. The default is False.

Returns

OrderedDict

Returns an ordered dictionary, sorted in decreasing order of similarity. The key is the (source, sink) tuple, and the value is the computed similarity score.

Returns

int

Returns the number of singleton nodes.

Returns

SAS graph object

Returns a directed copy of the input graph.

Returns

SAS graph object

Returns an immutable SAS graph object.

Returns

SAS graph object

Returns a mutable SAS graph object.

Parameters

data : bool or list, optional

Specifies whether or not to retain attributes. The default is True. When the value is True (or when a list is given), the Pandas DataFrame includes all edge attributes (or all listed edge attributes).

Returns

dataframe

Returns a Pandas DataFrame that includes the graph edges.

Parameters

data : bool or list, optional

Specifies whether or not to retain attributes. The default is True. When the value is True (or when a list is given), the Pandas DataFrame includes all the node attributes (or all the listed attributes).

Returns

dataframe

Returns a Pandas DataFrame that includes the graph nodes.

Returns

SAS graph object

Returns a directed copy of the input graph.

Yields

generator

Yields a generator of nodes in topological order. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Returns

SAS graph object

Returns the transitive closure of the input graph that is returned as a SAS MultiGraph or MultiDiGraph object. This graph has the solution_summary attribute, which contains information about the results of the algorithm.

Returns

int

Returns the number of triangles.

Parameters

edge_weight : str or None, optional

Specifies the numeric edge attribute that corresponds to the edge weight. The default is None, which means that an unweighted TSP is calculated.

maxtime : float or None, optional

Specifies the maximum amount of time for solving a TSP. The default is None.

minobjective : float, optional

Specifies a minimum value such that when a solution is found whose objective is less than or equal to this value, the algorithm stops.

inplace : bool, optional

Specifies whether to add the TSP order values as attributes to the input graph directly or to create a copy of the graph. The default is False.

use_milp : bool, optional

Specifies whether or not to use a mixed integer linear programming (MILP) solver to solve a TSP. The default is True.

data : bool, optional

Specifies whether or not to retain attributes. When the value is True and the inplace parameter value is False (default values), the node and edge attributes of the graph are retained. This parameter has no effect when the inplace parameter is set to True.

Returns

SAS graph object or None

Returns a graph that has the solution_summary attribute, which contains information about the results of the algorithm. When the inplace parameter value is False, the returned graph is a Cycle that contains the calculated TSP tour edges. When the inplace parameter value is True, the graph is modified in place and None is returned. The modified graph contains the edge attributes tsp and tsp_order and the node attribute tsp_order.

Parameters

rhs : SAS graph object

Specifies the other graph, of the same type as self, with which to find the union.

nodes_attrs_agg : function or str or dict or None, optional

Specifies how to aggregate node attributes. The value can be a function, such as mean or np.sum; a string in the list {‘first’,’last’,’mean’}; or a dictionary that maps node attributes to functions. The default is None.

edges_attrs_agg : function or str or dict or None, optional

Specifies how to aggregate edge attributes. The value can be a function, such as mean or np.sum; a string in the list {‘first’,’last’,’mean’}; or a dictionary that maps edge attributes to functions. The default is None.

Returns

SAS graph object

Returns a graph that is constructed by the union of the two graphs.

Parameters

capacity : float

Specifies the capacity of each vehicle.

depot : node

Specifies the depot node for the vehicle routing problem.

node_demand : str or dict or iterable

Specifies the quantity of goods to deliver to or pick up from a customer. The default is ‘demand’.

edge_cost : str or dict or iterable

Specifies the cost of traversing each edge. The default is ‘weight’.

minroutes : int, optional

Specifies the minimum number of routes that are allowed to service demand.

maxroutes : int, optional

Specifies the maximum number of routes that are allowed to service demand.

maxtime : float or None, optional

Specifies the maximum amount of time for solving the vehicle routing problem. The default is None.

minobjective : float, optional

Specifies a minimum value such that when a solution is found whose objective is less than or equal to this value, the algorithm stops.

use_milp : bool, optional

Specifies whether or not to use a mixed integer linear programming (MILP) solver to solve the vehicle routing problem. The default is True.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of Cycle objects; each cycle represents one route. The generator has the solution_summary attribute, which contains information about the results of the algorithm.

Parameters

capacity : float

Specifies the capacity of each vehicle.

depot : node

Specifies the depot node for the vehicle routing problem.

node_demand : str or dict or iterable

Specifies the quantity of goods to deliver to or pick up from a customer. The default is ‘demand’.

edge_cost : str or dict or iterable

Specifies the cost of traversing each edge.

travel_time : str or dict or iterable

Specifies attributes or values that define the time that it takes to traverse each edge. The default is ‘weight’.

timewindow_lower : str or dict or iterable or None, optional

Specifies attributes or values that define the lower time limits within which a delivery vehicle can arrive at the customer nodes. The default is None.

timewindow_upper : str or dict or iterable or None, optional

Specifies attributes or values that define the upper time limits within which a delivery vehicle can arrive at the customer nodes. The default is None.

service_time : str or dict or iterable or None, optional

Specifies attributes or values that define the service time of the nodes. The default is None.

minroutes : int, optional

Specifies the minimum number of routes that are allowed to service demand.

maxroutes : int, optional

Specifies the maximum number of routes that are allowed to service demand.

maxtime : float or None, optional

Specifies the maximum amount of time for solving the vehicle routing problem. The default is None.

data : bool, optional

Specifies whether or not to retain attributes. The default is True, which means that the node and edge attributes of the graph are retained.

Yields

generator

Yields a generator of Cycle objects; each cycle represents one route. The generator has the solution_summary attribute, which contains information about the results of the algorithm.