Network Action Set

Finding the Biconnected Components of an Undirected Graph

This section contains PROC CAS code.

Note: Input data must be accessible in your CAS session, either as a CAS table or as a transient-scope table. A CAS table has a two-level name: the first level is your CAS engine libref, and the second level is the table name. You refer to this table in the CAS procedure by specifying only the second level. For more information about two-level names, see Chapter 2, Shared Concepts (SAS Viya: Machine Learning Procedures). A transient-scope table is called directly from the action and exists in memory for the duration of the action. For more information about accessing data, see SAS Viya: System Programming Guide. For more information about PROC CAS and programming in CASL, see SAS Cloud Analytic Services: CASL Programmer’s Guide and SAS Cloud Analytic Services: CASL Reference.

This example illustrates the use of the biconnected components algorithm on the undirected graph G shown in Figure 1.

Figure 1: An Undirected Graph G

An Undirected Graph


The undirected graph G can be represented by the following links data set, LinkSetIn:

data LinkSetIn;
   input from $ to $ @@;
   datalines;
A B  A F  A G  B C  B D
B E  C D  E F  G I  G H
H I
;

The following DATA step loads the LinkSetIn data set into a CAS data table named mycas.LinkSetIn. These statements assume that the CAS engine libref is named mycas, but you can substitute any appropriately defined CAS engine libref.

data mycas.LinkSetIn;
   set LinkSetIn;
run;

The following statements calculate the biconnected components and articulation points for G and output the results in the data tables LinkSetOut and NodeSetOut:

proc cas;
   loadactionset "network";
   action network.biconnectedComponents result=r status=s /
      indexOffset = 1
      links       = {name = "LinkSetIn"}
      outNodes    = {name = "NodeSetOut", replace="true"}
      outLinks    = {name = "LinkSetOut", replace="true"};
   run;
   print r.ProblemSummary; run;
   print r.SolutionSummary; run;
   action table.fetch / table = "LinkSetOut" sortBy = {"biconcomp","from","to"}; run;
   action table.fetch / table = "NodeSetOut" sortBy = "node"; run;
quit;

The problem summary output from this action is shown in Output 28.1.1.

Output 28.1.1: Problem Summary

Problem Summary
Number of Nodes9
Number of Links11
Graph DirectionUndirected


The solution summary output from this action is shown in Output 28.1.2.

Output 28.1.2: Solution Summary

Solution Summary
Problem TypeBiconnected Components
Solution StatusOK
Number of Components4
Number of Articulation Points3
CPU Time0.00
Real Time0.00


The output data table LinkSetOut contains the biconnected components of the input graph, as shown in Output 28.1.3.

Output 28.1.3: Biconnected Components of an Undirected Graph

Selected Rows from Table LINKSETOUT
_Index_fromtobiconcomp
1AB1
2AF1
3BE1
4EF1
5AG2
6BC3
7BD3
8CD3
9GH4
10GI4
11HI4


The output data table NodeSetOut contains the articulation points of the input graph, as shown in Output 28.1.4.

Output 28.1.4: Articulation Points of an Undirected Graph

Selected Rows from Table NODESETOUT
_Index_nodeartpoint
1A1
2B1
3C0
4D0
5E0
6F0
7G1
8H0
9I0


The biconnected components are shown graphically in Output 28.1.5 and Output 28.1.6.

Output 28.1.5: Biconnected Components upper C Superscript 1 and upper C squared

upper C Superscript 1 upper C squared
biconcomp1_2 biconcomp1_3


Output 28.1.6: Biconnected Components upper C cubed and upper C Superscript 4

upper C cubed upper C Superscript 4
biconcomp1_1 biconcomp1_4


Finding the Biconnected Components of an Undirected Graph

This section contains Lua code for the analysis in the CASL version of this example, which contains details about the results.

Note: In order to run this code, the data that are described in the CASL version need to be accessible to the CAS server. One way to do this is to convert the LinkSetIn data to the comma-separated-value (CSV) file LinkSetIn.csv and then use the following code to load the CSV file into CAS:

s:loadtable{casLib="casuser", path="LinkSetIn.csv"}

For more information about coding in Lua, see Getting Started with SAS Viya for Lua and SAS Viya: System Programming Guide.

The following statements calculate the biconnected components and articulation points for G and output the results in the data tables LinkSetOut and NodeSetOut:

s:network_biconnectedComponents{
   indexOffset = 1,
   links       = {name = "LinkSetIn"},
   outNodes    = {name = "NodeSetOut", replace=true},
   outLinks    = {name = "LinkSetOut", replace=true}}

Finding the Biconnected Components of an Undirected Graph

This section contains Python code for the analysis in the CASL version of this example, which contains details about the results.

Note: In order to run this code, the data that are described in the CASL version need to be accessible to the CAS server. One way to do this is to convert the LinkSetIn data to the comma-separated-value (CSV) file LinkSetIn.csv and then use the following code to load the CSV file into CAS:

s.upload_file('LinkSetIn.csv')

For more information about coding in Python, see Getting Started with SAS Viya for Python and SAS Viya: System Programming Guide.

The following statements calculate the biconnected components and articulation points for G and output the results in the data tables LinkSetOut and NodeSetOut:

s.network.biconnectedComponents(
    indexOffset = 1,
    links       = {"name":"LinkSetIn"},
    outNodes    = {"name":"NodeSetOut", "replace":True},
    outLinks    = {"name":"LinkSetOut", "replace":True})

Finding the Biconnected Components of an Undirected Graph

This example is not available for the R programming language.

Last updated: August 04, 2026