Assessing the consistency of community structure in complex networks

TL;DR

This paper introduces scaled inclusivity, a new method to measure the consistency of community structures at the node level across multiple networks, applicable both cross-sectionally and longitudinally.

Contribution

The paper presents scaled inclusivity, a novel approach for quantifying node-level community structure changes across networks, addressing limitations of existing methods focused on community or network-wide changes.

Findings

Scaled inclusivity yields reasonable results for simulated networks.

The method effectively assesses community consistency in real-world networks.

It can be applied both cross-sectionally and longitudinally.

Abstract

In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze changing communities, but most of these are limited to evolution of a single network over time. In addition, most of the existing methods are more concerned with change at the community level than at the level of the individual node. In this paper, we introduce scaled inclusivity, which is a method to quantify the change in community structure across networks. Scaled inclusivity evaluates the consistency of the classiffication of every node in a network independently. In addition, the method can be applied cross-sectionally as well as longitudinally. In this paper, we calculate the scaled inclusivity for a set of simulated networks of United States cities and a set of real networks consisting of teams that play in the top division of American college football. We found that scaled inclusivity yields reasonable results for the consistency of individual nodes in both sets of networks. We propose that scaled inclusivity may provide a useful way to quantify the change in a network's community structure.