Modularity in Complex Multilayer Networks with Multiple Aspects: A Static Perspective

TL;DR

This paper introduces a static multilayer network model with multiple aspects, derives a modularity function for community detection, and proposes a spectral optimization method, demonstrating its effectiveness on real-world networks.

Contribution

It presents a new multilayer network model with multiple aspects, derives a modularity function from a static perspective, and introduces a spectral method for community detection.

Findings

The proposed method effectively detects communities in multilayer networks.

Experiments show reliable performance on electroencephalograph and other empirical networks.

The modularity function provides insights into community quality in multilayer systems.

Abstract

Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem - community detection - in multilayer networks are still limited. In this work, we first introduce the multilayer network model representation with multiple aspects, which is flexible to a variety of networks. Then based on this model, we naturally derive the multilayer modularity - a widely adopted objective function of community detection in networks - from a static perspective as an evaluation metric to evaluate the quality of the communities detected in multilayer networks. It enables us to better understand the essence of the modularity by pointing out the specific kind of communities that will lead to a high modularity score. We also propose a spectral method called mSpec for the optimization of the proposed modularity function based on the supra-adjacency representation of the multilayer networks. Experiments on the electroencephalograph network and the comparison results on several empirical multilayer networks demonstrate the feasibility and reliable performance of the proposed method.