# Structural measures for multiplex networks

arXiv: https://arxiv.org/abs/1308.3182 · HTML: https://mlsanity.com/paper/1308.3182/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2013.

## Built on by (most cited first, 6 of 6)

- [mGNN: Generalizing the Graph Neural Networks to the Multilayer Case](https://mlsanity.com/paper/2109.10119/) (2021)
- [Universal Multilayer Network Exploration by Random Walk with Restart](https://mlsanity.com/paper/2107.04565/) (2021)
- [A Tensor-Based Formulation of Hetero-functional Graph Theory](https://mlsanity.com/paper/2101.07220/) (2021)
- [MultiSAGE: a multiplex embedding algorithm for inter-layer link prediction](https://mlsanity.com/paper/2206.13223/) (2022)
- [Cognitive modelling with multilayer networks: Insights, advancements and future challenges](https://mlsanity.com/paper/2210.00500/) (2022)
- [MPXGAT: An Attention based Deep Learning Model for Multiplex Graphs Embedding](https://mlsanity.com/paper/2403.19246/) (2024)

## Abstract (arXiv)

Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes, rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular we propose a series of measures to characterize the multiplexicity of the systems in terms of: i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, ii) local properties such as the clustering coefficient and the transitivity, iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuine multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications and business relationships.