Centrality Metrics-Based Connected Dominating Sets for Real-World Network Graphs

Abstract

The authors investigate the use of centrality metrics as node weights to determine connected dominating sets (CDS) for a suite of 60 real-world network graphs of diverse degree distribution. They employ centrality metrics that are neighborhood-based (degree centrality [DEG] and eigenvector centrality [EVC]), shortest path-based (betweenness centrality [BWC] and closeness centrality [CLC]) as well as the local clustering coefficient complement-based degree centrality metric (LCC'DC), which is a hybrid of the neighborhood and shortest path-based categories. The authors target for minimum CDS node size (number of nodes constituting the CDS). Though both the BWC and CLC are shortest path-based centrality metrics, they observe the BWC-based CDSs to be of the smallest node size for about 60% of the real-world networks and the CLC-based CDSs to be of the largest node size for more than 40% of the real-world networks. The authors observe the computationally light LCC'DC-based CDS node size to be the same as the computationally heavy BWC-based CDS node size for about 50% of the real-world networks.