Modeling and Measuring Graph Similarity: The Case for Centrality Distance

TL;DR

This paper introduces a novel similarity measure for complex networks called centrality distance, which quantifies differences based on node centrality, and demonstrates its effectiveness in distinguishing network evolution paths.

Contribution

It proposes the centrality distance metric for comparing complex graphs, focusing on node roles, and applies it to analyze social network evolution.

Findings

Centrality distance effectively differentiates between random and real network evolution.

The measure captures the importance of node roles in network comparison.

Application to social networks shows practical utility.

Abstract

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks. However, surprisingly little is known today about models to compare complex graphs, and quantitatively measure their similarity. This paper proposes a natural similarity measure for complex networks: centrality distance, the difference between two graphs with respect to a given node centrality. Centrality distances allow to take into account the specific roles of the different nodes in the network, and have many interesting applications. As a case study, we consider the closeness centrality in more detail, and show that closeness centrality distance can be used to effectively distinguish between randomly generated and actual evolutionary paths of two dynamic social networks.