Measuring robustness of community structure in complex networks

TL;DR

This paper introduces a mathematically grounded method to measure the robustness of community structures in complex networks using the critical resolution parameter, with practical computation via a co-evolution model.

Contribution

It proposes a novel, theoretically validated index for robustness based on the critical resolution parameter, and offers an efficient computational method using a co-evolution model.

Findings

The index is inversely proportional to community robustness.

The method is applicable to broad clustering problems in network analysis.

Experimental results demonstrate the effectiveness of the approach.

Abstract

The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, $\gamma_C$, to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of $\gamma_C$. The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.