# Combinatorial Analysis of Multiple Networks

arXiv: https://arxiv.org/abs/1303.4986 · HTML: https://mlsanity.com/paper/1303.4986/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2013.

## Built on by (most cited first, 9 of 9)

- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [A Latent Space Model for Multilayer Network Data](https://mlsanity.com/paper/2102.09560/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Systematic assessment of the quality of fit of the stochastic block model for empirical networks](https://mlsanity.com/paper/2201.01658/) (2022)
- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [Mind the Links: Cross-Layer Attention for Link Prediction in Multiplex Networks](https://mlsanity.com/paper/2509.23409/) (2025)
- [Estimating mixed memberships in multi-layer networks](https://mlsanity.com/paper/2404.03916/) (2024)
- [Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks](https://mlsanity.com/paper/2405.06884/) (2024)
- [A Transfer Learning Framework for Multilayer Networks via Model Averaging](https://mlsanity.com/paper/2506.12455/) (2025)

## Abstract (arXiv)

The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the development of multi-layer networks. These models have the potential of becoming the reference tools in network data analysis, but require the parallel development of specific analysis methods explicitly exploiting the information hidden in-between the layers and the availability of a critical mass of reference data to experiment with the tools and investigate the real-world organization of these complex systems. In this work we introduce a real-world layered network combining different kinds of online and offline relationships, and present an innovative methodology and related analysis tools suggesting the existence of hidden motifs traversing and correlating different representation layers. We also introduce a notion of betweenness centrality for multiple networks. While some preliminary experimental evidence is reported, our hypotheses are still largely unverified, and in our opinion this calls for the availability of new analysis methods but also new reference multi-layer social network data.