Multiplexons: Limits of Multiplex Networks

2025-10-08

AI Summary

This study addresses the lack of rigorous limit theory for large-scale multilayer networks by establishing the first “multion” limit framework for dense multilayer networks, systematically extending graphon theory to multilayer settings. Methodologically, it integrates functional analysis and probabilistic graph theory to define convergence and construct appropriate metrics, validating the framework on canonical models—including Erdős–Rényi multilayer graphs, inhomogeneous random multilayer graphs, and dynamic multilayer networks. Key contributions include: (i) the first unified limit expressions for fundamental structural metrics—such as degree distribution and clustering coefficient—in multilayer networks; (ii) a characterization of their convergence本质 within the decorated graph framework; and (iii) a scalable theoretical foundation for modeling and analyzing heterogeneous interactions in social, industrial, and biological systems. The work further identifies promising directions, including higher-order dependency modeling and dynamic limit theory for evolving multilayer networks.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to the widespread coexistence of diverse interactions in social, industrial, and biological domains. This motivates the development of a rigorous and readily applicable framework for studying properties of large multiplex networks. In this article, we provide a self-contained introduction to the limit theory of dense multiplex networks, analogous to the theory of graphons (limit theory of dense graphs). As applications, we derive limiting analogues of commonly used multiplex features, such as degree distributions and clustering coefficients. We also present a range of illustrative examples, including correlated versions of Erdős-Rényi and inhomogeneous random graph models and dynamic networks. Finally, we discuss how multiplex networks fit within the broader framework of decorated graphs, and how the convergence results can be recovered from the limit theory of decorated graphs. Several future directions are outlined for further developing the multiplex limit theory.

Problem

• Developing limit theory for dense multiplex networks
• Establishing rigorous framework for large multiplex analysis
• Extending graphon theory to multiplex network structures

Innovation

• Develops limit theory for dense multiplex networks
• Extends graphon theory to multilayer network structures
• Applies framework to correlated random graph models