Latent Network Features and Overlapping Community Discovery via Boolean Intersection Representations

TL;DR

This paper introduces a novel Boolean feature model for complex networks using Boolean intersection representations, enabling the discovery of overlapping communities and node features with theoretical bounds and algorithms.

Contribution

It presents a new Boolean intersection-based model for network communities, including bounds, characterizations, and algorithms for cointersection representations.

Findings

Derived bounds on the number of features needed for cointersection representations

Characterized graph families with exact cointersection representations

Developed algorithms for optimal and approximate cointersection discovery

Abstract

We propose a new latent Boolean feature model for complex networks that captures different types of node interactions and network communities. The model is based on a new concept in graph theory, termed the Boolean intersection representation of a graph, which generalizes the notion of an intersection representation. We mostly focus on one form of Boolean intersection, termed cointersection, and describe how to use this representation to deduce node feature sets and their communities. We derive several general bounds on the minimum number of features used in cointersection representations and discuss graph families for which exact cointersection characterizations are possible. Our results also include algorithms for finding optimal and approximate cointersection representations of a graph.