Efficient Antagonistic $k$k-Plex Enumeration in Signed Graphs

Abstract

A signed graph is a graph where each edge receives a sign, positive or negative. The signed graph model has been used in many real applications, such as protein complex discovery and social network analysis. Finding cohesive subgraphs in signed graphs is a fundamental problem. A $k$-plex is a common model for cohesive subgraphs in which every vertex is adjacent to all but at most $k$ vertices within the subgraph. In this paper, we propose the model of size-constrained antagonistic $k$-plex in a signed graph. The proposed model guarantees that the resulting subgraph is a $k$-plex and can be divided into two sub-$k$-plexes, both of which have positive inner edges and negative outer edges. This paper aims to identify all maximal antagonistic $k$-plexes in a signed graph. Through rigorous analysis, we show that the problem is NP-Hardness. We propose a novel framework for maximal antagonistic $k$-plexes utilizing set enumeration. Efficiency is improved through pivot pruning and early termination based on the color bound. Preprocessing techniques based on degree and dichromatic graphs effectively narrow the search space before enumeration. Extensive experiments on real-world datasets demonstrate our algorithm’s efficiency, effectiveness, and scalability.