FirmCore Decomposition of Multilayer Networks

TL;DR

This paper introduces FirmCore, a polynomial-time dense subgraph decomposition method for multilayer networks, enabling efficient analysis and approximation of densest subgraphs in complex, multi-aspect graph data.

Contribution

The paper presents FirmCore, a novel polynomial-time dense subgraph decomposition for multilayer networks, extending to directed graphs, with improved efficiency and solution quality over existing methods.

Findings

FirmCore is significantly more efficient than existing algorithms.

FirmCore provides solutions of equal or better quality for densest subgraph problems.

The method extends to directed multilayer graphs, broadening applicability.

Abstract

A key graph mining primitive is extracting dense structures from graphs, and this has led to interesting notions such as $k$-cores which subsequently have been employed as building blocks for capturing the structure of complex networks and for designing efficient approximation algorithms for challenging problems such as finding the densest subgraph. In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects. Multilayer (ML) networks have been proposed for accurately modeling such applications. In this paper, we present FirmCore, a new family of dense subgraphs in ML networks, and show that it satisfies many of the nice properties of $k$-cores in single-layer graphs. Unlike the state of the art core decomposition of ML graphs, FirmCores have a polynomial time algorithm, making them a powerful tool for understanding the structure of massive ML networks. We also extend FirmCore for directed ML graphs. We show that FirmCores and directed FirmCores can be used to obtain efficient approximation algorithms for finding the densest subgraphs of ML graphs and their directed counterparts. Our extensive experiments over several real ML graphs show that our FirmCore decomposition algorithm is significantly more efficient than known algorithms for core decompositions of ML graphs. Furthermore, it returns solutions of matching or better quality for the densest subgraph problem over (possibly directed) ML graphs.