A Parameterized Centrality Metric for Network Analysis

TL;DR

This paper introduces a normalized alpha-centrality metric with a tunable parameter for network analysis, enhancing node ranking and community detection by capturing local and global importance, demonstrated on benchmark networks.

Contribution

It proposes a normalized, parameterized alpha-centrality metric and extends modularity-based community detection to improve network structure analysis.

Findings

Better identification of important nodes at different scales

Enhanced community detection results on benchmark networks

Provides deeper insights into network structure

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.