The OPTGRAPH Procedure

This example uses the same data as are used in the section Influence Centrality for Project Groups in a Research Department, which illustrates influence centrality by considering the link weights that represent some measure of reporting magnitude. In Influence Centrality for Project Groups in a Research Department, links between managers (or leads) and direct reports had higher link weights than links between non-managers. This interpretation makes sense in the context of influence centrality because weight and the metric are directly related. However, weight and the metric are inversely related for closeness and betweenness centrality.

This example considers the speed of the flow of information between people. In this sense, connections between managers and direct reports have smaller values, which cost less in the shortest path calculations. The following DATA step produces a new links data set, based on LinkSetInDept, which uses the inverse of the weight:

data LinkSetInDeptInv;
   set LinkSetInDept;
   weight = 1 / weight;
run;

The following statements calculate weighted (and unweighted) closeness and betweenness centrality. Notice that this example also uses the NTHREADS= option in the PERFORMANCE statement to specify two threads to allow the computation to be run in parallel. Since these data have 18 nodes, each thread can process 9 nodes simultaneously.

proc optgraph
   loglevel     = moderate
   data_links   = LinkSetInDeptInv
   out_links    = LinkSetOut
   out_nodes    = NodeSetOut;
   performance
      nthreads  = 2;
   centrality
      close     = both
      between   = both;
run;
%put &_OPTGRAPH_;
%put &_OPTGRAPH_CENTRALITY_;

The progress of the procedure is shown in Output 1.4.1.

The node data set NodeSetOut shows the weighted and unweighted closeness and node betweenness centrality, as shown in Output 1.4.2.

The link data set LinkSetOut shows the weighted and unweighted link betweenness centrality, as shown in Output 1.4.3.

Note that Chapman (director) and Yu (manager, reporting to Chapman) both have the highest weighted closeness centrality. However, Yu’s weighted betweenness centrality is highest because he serves as more of a gatekeeper between his three groups (D4a, D4b, and D4c) and the rest of the department.