Modularity in Multilayer Networks using Redundancy-based Resolution and Projection-based Inter-Layer Coupling
arXiv:1906.12204 · doi:10.1109/TNSE.2019.2913325
Abstract
The generalized version of modularity for multilayer networks, a.k.a. multislice modularity, is characterized by two model parameters, namely resolution factor and inter-layer coupling factor. The former corresponds to a notion of layer-specific relevance, whereas the inter-layer coupling factor represents the strength of node connections across the network layers. Despite the potential of this approach, the setting of both parameters can be arbitrarily selected, without considering specific characteristics from the topology of the multilayer network as well as from an available community structure. Also, the multislice modularity is not designed to explicitly model order relations over the layers, which is of prior importance for dynamic networks. This paper aims to overcome the main limitations of the multislice modularity by introducing a new formulation of modularity for multilayer networks. We revise the role and semantics of both the resolution and inter-layer coupling factors based on information available from the within-layer and inter-layer structures of the multilayer communities. Also, our proposed multilayer modularity is general enough to consider orderings of network layers and their constraints on layer coupling. Experiments were carried out on synthetic and real-world multilayer networks using state-of-the-art approaches for multilayer community detection. The obtained results have shown the meaningfulness of the proposed modularity, revealing the effects of different combinations of the resolution and inter-layer coupling functions. This work also represents a starting point for the development of new optimization methods for community detection in multilayer networks.
arXiv admin note: substantial text overlap with arXiv:1709.07253
References in corpus (29)
- Finding and evaluating community structure in networks
- Modularity and community structure in networks
- Community detection in graphs
- Finding community structure in very large networks
- Fast algorithm for detecting community structure in networks
- Multilayer Networks
- The structure and dynamics of multilayer networks
- Resolution limit in community detection
- Analysis of weighted networks
- Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
- Statistical Mechanics of Community Detection
- Community detection in networks: A user guide
- Community detection in complex networks using Extremal Optimization
- Community structure in directed networks
- Modularity and community detection in bipartite networks
- Layer aggregation and reducibility of multilayer interconnected networks
- Community detection in networks with positive and negative links
- Analysis of the structure of complex networks at different resolution levels
- Module identification in bipartite and directed networks
- Extending the definition of modularity to directed graphs with overlapping communities
- Size reduction of complex networks preserving modularity
- Community Detection via Maximization of Modularity and Its Variants
- A Classification for Community Discovery Methods in Complex Networks
- Analysis of community structure in networks of correlated data
- Clustering Network Layers With the Strata Multilayer Stochastic Block Model
- The nested structural organization of the worldwide trade multi-layer network
- Unfolding the complexity of the global value chain: Strengths and entropy in the single-layer, multiplex, and multi-layer international trade networks
- Limitation of multi-resolution methods in community detection
- Multi-resolution community detection based on generalized self-loop rescaling strategy