Detecting Important Nodes to Community Structure Using the Spectrum of the Graph

TL;DR

This paper introduces a spectral-based method to identify important nodes in networks that influence community structure, distinguishing core nodes from bridges with high accuracy and efficiency.

Contribution

A novel spectral centrality metric is proposed to evaluate node importance to communities, including a way to differentiate core nodes from bridges.

Findings

Effective in artificial and real-world networks

Accurately identifies core and bridge nodes

Provides a fast, spectrum-based approach

Abstract

Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem. In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change in the eigenvalues of the network adjacency matrix upon their removal. Second, we also propose an index to distinguish two kinds of important nodes in communities, i.e., "community core" and "bridge". Our indices are only relied on the spectrum of the graph matrix. They are applied in many artificial networks as well as many real-world networks. This new methodology gives us a basic approach to solve this challenging problem and provides a realistic result.