A Parameterized Centrality Metric for Network Analysis

Abstract

A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], 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, specifically, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method [Newman and Girvan, 2004] 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. By 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 method to several benchmark networks and show that it leads to better insight into network structure than alternative methods.

11 pages, submitted to Physical Review E

References in corpus (7)

• Community detection in graphs
• Finding community structure in networks using the eigenvectors of matrices
• Cooperative Game Theory Approaches for Network Partitioning
• Community structure in directed networks
• Classes of complex networks defined by role-to-role connectivity profiles
• Creative elements: network-based predictions of active centres in proteins, cellular and social networks
• Motif-based communities in complex networks

Cited by in corpus (7)

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• Spectral Clustering with Epidemic Diffusion
• Characterising heavy-tailed networks using q-generalised entropy and q-adjacency kernels
• Community Detection via Katz and Eigenvector Centrality
• Adjustable reach in a network centrality based on current flows