Parameterized Centrality for Network Analysis
Bonacich centrality measures the number of attenuated paths between nodes in a network. We use this metric to study network structure, specifically, to rank nodes and find community structure of the network. To this end we extend the modularity-maximization method for community detection to use this centrality metric as a measure of node connectivity. Bonacich centrality contains a tunable parameter that sets the length scale of interactions. By studying how rankings and discovered communities change when this parameter is varied allows us to identify globally important nodes and structures. We apply the proposed method to several benchmark networks and show that it leads to better insight into network structure than earlier methods.