The NETWORK Procedure
Example 2.7 Recursive Community Detection on Zachary’s Karate Club Data
This example illustrates the use of the RECURSIVE option in PROC NETWORK for community detection on Zachary’s Karate Club data (Zachary 1977). The data table appears in Community Detection on Zachary’s Karate Club Data. The current example forces each community to contain no more than five nodes and limits the number of links between any pair of nodes within any community to be no greater than 2.
proc network
links = mycas.LinkSetIn
outNodes = mycas.NodeSetOut;
community
resolutionList = 1.0
recursive (maxCommSize = 5 maxDiameter = 2 relation = AND)
outCommunity = mycas.CommOut;
run;
The output data table mycas.NodeSetOut contains the community identifier of each node, as shown in Output 2.7.1.
Output 2.7.1: Community Nodes Output
| node | community_1 |
|---|---|
| 0 | 4 |
| 1 | 7 |
| 2 | 8 |
| 3 | 6 |
| 4 | 5 |
| 5 | 1 |
| 6 | 1 |
| 7 | 1 |
| 8 | 6 |
| 9 | 3 |
| 10 | 6 |
| 11 | 1 |
| 12 | 7 |
| 13 | 5 |
| 14 | 5 |
| 15 | 2 |
| 16 | 2 |
| 17 | 1 |
| 18 | 8 |
| 19 | 2 |
| 20 | 8 |
| 21 | 4 |
| 22 | 7 |
| 23 | 2 |
| 24 | 9 |
| 25 | 9 |
| 26 | 9 |
| 27 | 4 |
| 28 | 9 |
| 29 | 10 |
| 30 | 4 |
| 31 | 3 |
| 32 | 10 |
| 33 | 2 |
The output data table mycas.CommOut contains the number of nodes in each community, as shown in Output 2.7.2.
Output 2.7.2: Community Number of Nodes Output
| level | resolution | community | nodes | intra_links | inter_links | density | cut_ratio | conductance |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 5 | 6 | 4 | 0.60000 | 0.02759 | 0.25000 |
| 1 | 1 | 2 | 5 | 4 | 12 | 0.40000 | 0.08276 | 0.60000 |
| 1 | 1 | 3 | 2 | 1 | 7 | 1.00000 | 0.10938 | 0.77778 |
| 1 | 1 | 4 | 4 | 4 | 17 | 0.66667 | 0.14167 | 0.68000 |
| 1 | 1 | 5 | 3 | 2 | 9 | 0.66667 | 0.09677 | 0.69231 |
| 1 | 1 | 6 | 3 | 2 | 12 | 0.66667 | 0.12903 | 0.75000 |
| 1 | 1 | 7 | 3 | 2 | 15 | 0.66667 | 0.16129 | 0.78947 |
| 1 | 1 | 8 | 3 | 2 | 10 | 0.66667 | 0.10753 | 0.71429 |
| 1 | 1 | 9 | 4 | 4 | 7 | 0.66667 | 0.05833 | 0.46667 |
| 1 | 1 | 10 | 2 | 1 | 7 | 1.00000 | 0.10938 | 0.77778 |
The community graph is shown in Figure 196, with different node shapes and colors representing different communities.
Figure 196: Karate Club Recursive Communities
As you can see from Output 2.7.2, Community 4, whose nodes are drawn as black ellipses in Figure 196, contains seven nodes even though the maximum number of nodes in any community is set to 5. This is because Community 4 has a symmetric shape: Nodes 0 and 33 are in the center, and they symmetrically connect to Nodes 21, 15, 19, 16, and 23. Therefore, this community cannot be further split.