Counting Small Balanced (p,q)-bicliques in Signed Bipartite Graphs

TL;DR

This paper introduces new algorithms for counting small balanced (p,q)-bicliques in signed bipartite graphs, improving efficiency over existing methods through vertex-based pruning.

Contribution

It presents two novel algorithms, BBWC and BBVP, for efficiently counting balanced bicliques in signed bipartite graphs, extending existing unsigned graph techniques.

Findings

BBVP outperforms baseline SBCList++ with 636× speedup for p=q=3.

Extended BCList++ to incorporate edge signs for signed bipartite graphs.

Extensive experiments on real-world datasets validate the efficiency of BBVP.

Abstract

Two disjoint sets of entities and their relationship can be modelled as a bipartite graph. Real-life examples include drug-target interaction in biological networks, user-item relationships in e-commerce networks, etc. Motif-based analysis is essential for understanding the structure of large-scale networks, and bipartite graphs are no exception. In contrast to unsigned graphs, motif analysis in signed bipartite graphs has received limited attention. The smallest non-trivial motif in a signed bipartite graph is a balanced (2,2)-biclique, often called a balanced butterfly, which captures only local patterns and cannot reveal higher-order relationships. Bipartite motifs have been studied in the literature in the context of signed bipartite graphs, such as maximal biclique, bitruss, and so on. None of these works addresses bipartite motifs with fixed-sized vertex sets, which are often relevant in practical situations. In this work, we study the balanced (p,q)-biclique counting problem for small values of p and q. As a baseline, we first adapt and extend the state-of-the-art BCList++ algorithm for unsigned bipartite graphs to incorporate edge signs, which we call SBCList++. We then propose two efficient algorithms: BBWC, a wedge-centric approach that enforces balance constraints during enumeration, and BBVP, a vertex-based pruning approach that directly enumerates feasible vertex sets. Extensive experiments on large real-world datasets demonstrate that the vertex-based pruning algorithm, BBVP, significantly outperforms the baseline, achieving an average speedup of 636$\times$ over SBCList++ (where p=q=3).