Louvain-like Methods for Community Detection in Multi-Layer Networks

In many complex systems, entities interact with each other through complicated patterns that embed different relationships, thus generating networks with multiple levels and/or multiple types of edges. When trying to improve our understanding of those complex networks, it is of paramount importance to explicitly take the multiple layers of connectivity into account in the analysis. In this paper, we focus on detecting community structures in multi-layer networks, i.e., detecting groups of well-connected nodes shared among the layers, a very popular task that poses a lot of interesting questions and challenges. Most of the available algorithms in this context either reduce multi-layer networks to a single-layer network or try to extend algorithms for single-layer networks by using consensus clustering. Those approaches have anyway been criticized lately. They indeed ignore the connections among the different layers, hence giving low accuracy. To overcome these issues, we propose new community detection methods based on tailored Louvain-like strategies that simultaneously handle the multiple layers. We consider the informative case, where all layers show a community structure, and the noisy case, where some layers only add noise to the system. We report experiments on both artificial and real-world networks showing the effectiveness of the proposed strategies.Comment: 16 pages, 4 figure

Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods, which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques

Discovering Community Structure in Multilayer Networks

International audienceCommunity detection in single layer, isolated networks has been extensively studied in the past decade. However, many real-world systems can be naturally conceptualized as multilayer networks which embed multiple types of nodes and relations. In this paper, we propose algorithm for detecting communities in multilayer networks. The crux of the algorithm is based on the multilayer modularity index Q_M, developed in this paper. The proposed algorithm is parameter-free, scalable and adaptable to complex network structures. More importantly, it can simultaneously detect communities consisting of only single type, as well as multiple types of nodes (and edges). We develop a methodology to create synthetic networks with benchmark multilayer communities. We evaluate the performance of the proposed community detection algorithm both in the controlled environment (with synthetic benchmark communities) and on the empirical datasets (Yelp and Meetup datasets); in both cases, the proposed algorithm outperforms the competing state-of-the-art algorithms