Dense and well-connected subgraph detection in dual networks

TL;DR

This paper introduces a novel polynomial-time method for detecting dense and well-connected subgraphs in dual networks, with applications in social media and neuroscience, by controlling connectivity constraints.

Contribution

It presents a new mathematical formulation based on k-edge connectivity for dual graph subgraph detection, enabling control over connectivity and density constraints, and demonstrates its practical utility.

Findings

Method outperforms state-of-the-art competitors.

Enables insightful analysis of Twitter user interactions.

Provides new understanding of brain networks in ASD.

Abstract

Dense subgraph discovery is a fundamental problem in graph mining with a wide range of applications \cite{gionis2015dense}. Despite a large number of applications ranging from computational neuroscience to social network analysis, that take as input a {\em dual} graph, namely a pair of graphs on the same set of nodes, dense subgraph discovery methods focus on a single graph input with few notable exceptions \cite{semertzidis2019finding,charikar2018finding,reinthal2016finding,jethava2015finding}. In this work, we focus the following problem: given a pair of graphs $G,H$ on the same set of nodes $V$, how do we find a subset of nodes $S \subseteq V$ that induces a well-connected subgraph in $G$ and a dense subgraph in $H$? Our formulation generalizes previous research on dual graphs \cite{Wu+15,WuZLFJZ16,Cui2018}, by enabling the {\em control} of the connectivity constraint on $G$. We propose a novel mathematical formulation based on $k$-edge connectivity, and prove that it is solvable exactly in polynomial time. We compare our method to state-of-the-art competitors; we find empirically that ranging the connectivity constraint enables the practitioner to obtain insightful information that is otherwise inaccessible. Finally, we show that our proposed mining tool can be used to better understand how users interact on Twitter, and connectivity aspects of human brain networks with and without Autism Spectrum Disorder (ASD).