Centrality in multilayer networks: accurate measurements with MultiNetPy

Abstract

The importance of a node, known as centrality, can be defined and measured in various ways. The main challenge of these measurements is their extension to multilayer networks. In multilayer networks, the influence of inter-layer edges compared to intra-layer edges must be considered when calculating centrality measures. Here, the primary purpose is to provide a multilayer network-specific framework to measure the importance of nodes, with special consideration for inter-layer edges and intra-layer ones. First, we considered the different centrality measures offered for multilayer networks, as well as the associated tools and packages. Next, we implemented some more informative measures specific to multilayer networks. The functionality of implemented metrics is provided for some real networks using Python. We assessed these metrics as ranking criteria and then contrasted the ranking results using three methods: intersection similarity, rank differences, and Kendall’s tau. The findings demonstrated that incorporating information from various layers enhances the effectiveness of the criteria. The final product is a publicly available Python package called MultiNetPy, available at https://github.com/Multinetpy/Multinetpy. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.