# Modularity in Multilayer Networks using Redundancy-based Resolution and Projection-based Inter-Layer Coupling

## TL;DR

This paper introduces a new multilayer network modularity formulation that better captures layer relevance, order relations, and community structure, improving community detection accuracy.

## Contribution

It revises the semantics of resolution and inter-layer coupling parameters and incorporates layer ordering, addressing limitations of existing multislice modularity.

## Key findings

- Proposed modularity outperforms existing methods on synthetic and real-world networks.
- Reveals the impact of different parameter combinations on community detection.
- Supports layer ordering in multilayer network analysis.

## 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.