Efficient Maximal Balanced CliPlex Enumeration in Signed Graphs

Renjie Sun, Chen Chen, Xiaoyang Wang, Wenjie Zhang, Ying Zhang, Xuemin Lin

Abstract: In signed graph analysis, the balanced clique model has received increasing attention recently. A clique is balanced, if it can be divided into two disjoint subgroups, where internal connections are positive and intergroup connections are negative. However, the requirement of fully negative intergroup connection is too strict, and it may fail to retrieve some important communities, considering the unbalanced distribution of positive and negative edges in real-world signed networks. Motivated by this, we leverage the concept of $k$-plex and propose a novel model, called Balanced $k$k-CliPlex ($k$-BCP), which relaxes the negative connections between two subgroups in a balanced clique. Given a signed graph, in this paper, we aim to enumerate all the maximal $k$-BCPs with a size constraint, which is proved to be NP-hard. To solve the problem, a reasonable baseline algorithm is first proposed by extending the existing approach for maximal balanced clique enumeration and equipped with two acceleration techniques. To scale for large graphs, we further introduce a partition method that can significantly reduce the search space, and propose three optimization strategies to filter unnecessary search branches during the enumeration. Comprehensive experiments are conducted over 10 real-world networks to demonstrate the efficiency and effectiveness of the proposed techniques and model.

External IDs:dblp:journals/tkde/SunCWZZL26