NETWORK Procedure

This section briefly introduces some common notation and assumptions that are used throughout the chapter. Let define a graph (or multigraph) that contains a set N of nodes and a set E of links. Table 8 provides a list of commonly used notation.

Table 8: Common Notation

Notation	Description
	The set of links that are incident to node i
	The set of outgoing links that are connected from node i
	The set of incoming links that are connected to node i
	The from node of link e
	The to node of link e
	The set of neighbors (that is, unique nodes that are connected by links incident with node i)
	The multiset of neighbors (that is, nodes that are connected by links incident with node i)
	The set of neighbors, excluding node i itself (that is, unique nodes that are connected by links, excluding self-links, incident with node i)
	The set of out-neighbors (that is, unique nodes that are connected by outgoing links from node i)
	The multiset of out-neighbors (that is, nodes that are connected by outgoing links from node i)
	The set of out-neighbors, excluding node i itself (that is, unique nodes that are connected by outgoing links, excluding self-links, from node i)
	The set of in-neighbors (that is, unique nodes that are connected by incoming links to node i)
	The set of in-neighbors, excluding node i itself (that is, unique nodes that are connected by incoming links, excluding self-links, to node i)

A complete graph on node set N is a simple graph (with no self-links) in which every pair of nodes in N is connected by a link. The number of links in a complete graph on node set N is

when DIRECTION=UNDIRECTED, or

when DIRECTION=DIRECTED.

An induced subgraph of a graph is a subgraph that is defined by a subset of nodes and the links of G whose endpoints are both in the subset S.