Parameterized centrality metric for network analysis.

A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [P. Bonacich, Am. J. Sociol. 92, 1170 (1987)], measures the number of attenuated paths that exist between nodes. We introduce a normalized version of this metric and use it to study network structure, for example, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method for community detection to use this metric as the measure of node connectivity. Normalized alpha-centrality is a powerful tool for network analysis, since it contains a tunable parameter that sets the length scale of interactions. Studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures. We apply the proposed metric to several benchmark networks and show that it leads to better insights into network structure than alternative metrics.