Inference for decorated graphs and application to multiplex networks

TL;DR

This paper introduces a novel inference method for decorated graphons, enabling the analysis of complex networks with richer edge information, such as weights and types, which was not possible with traditional graphon techniques.

Contribution

The paper develops the first inference technique for decorated graphons, extending traditional graphon estimation to handle richer relational data in complex networks.

Findings

The proposed method is consistent with non-parametric theory for finite decoration spaces.

Simulations show the method achieves theoretical convergence rates in practice.

Application to synthetic and empirical data demonstrates improved network modeling.

Abstract

A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are clear, they traditionally are used for describing only binary edge information, which limits their utility for more complex relational data. Decorated graphons were introduced to extend the graphon framework by incorporating richer relationships, such as edge weights and types. This specificity in modelling connections provides more granular insight into network dynamics. Yet, there are no existing inference techniques for decorated graphons. We develop such an estimation method, extending existing techniques from traditional graphon estimation to accommodate these richer interactions. We derive the rate of convergence for our method and show that it is consistent with traditional non-parametric theory when the decoration space is finite. Simulations confirm that these theoretical rates are achieved in practice. Our method, tested on synthetic and empirical data, effectively captures additional edge information, resulting in improved network models. This advancement extends the scope of graphon estimation to encompass more complex networks, such as multiplex networks and attributed graphs, thereby increasing our understanding of their underlying structures.