Graphon-aided Joint Estimation of Multiple Graphs

TL;DR

This paper introduces a novel method for jointly estimating multiple network topologies using graphons, enabling inference across graphs of different sizes and alignments, validated through synthetic and real data.

Contribution

It proposes a graphon-based joint estimation framework that handles unaligned and differently sized graphs, extending existing network inference techniques.

Findings

Outperforms existing methods on synthetic datasets.

Effective in real-world network inference tasks.

Handles graphs with different sizes and no node alignment.

Abstract

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is a nonparametric model from which graphs of potentially different sizes can be drawn. The versatility of graphons allows us to tackle the joint inference problem even for the cases where the graphs to be recovered contain different number of nodes and lack precise alignment across the graphs. Our solution is based on combining a maximum likelihood penalty with graphon estimation schemes and can be used to augment existing network inference methods. We validate our proposed approach by comparing its performance against competing methods in synthetic and real-world datasets.