Centrality-based identification of important edges in complex networks

TL;DR

This paper introduces a new approach to measure and analyze the importance of edges in complex networks using centrality concepts, enabling hierarchical network decomposition.

Contribution

It extends vertex centrality metrics to edges and proposes a hierarchy-based decomposition method for identifying important edges in networks.

Findings

Effective in various network models

Identifies key edges in social networks

Detects important edges in brain networks

Abstract

Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis as well as in evolving epileptic brain networks.