Algorithm

Discrete mathematics

Theoretical computer science

Scalability

Computer science

Mathematical optimization

Complex network

Database

Graph

Mathematics

Clique percolation method

Leverage (statistics)

Artificial intelligence

Clique

Combinatorics

1-planar graph

Clique problem

Enumeration

Chordal graph

Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. In real world, however, many applications are modeled as signed networks with positive and negative edges. As the signed networks hold their own properties different from the unsigned networks, the existing clique model is inapplicable for the signed networks. Motivated by this, we propose the balanced clique model that considers the most fundamental and dominant theory, structural balance theory, for signed networks, and study the maximal balanced clique enumeration problem which computes all the maximal balanced cliques in a given signed network. We show that the maximal balanced clique enumeration problem is NP-Hard. A straightforward solution for the maximal balanced clique enumeration problem is to treat the signed network as two unsigned networks and leverage the off-the-shelf techniques for unsigned networks. However, such a solution is inefficient for large signed networks. To address this problem, in this paper, we first propose a new maximal balanced clique enumeration algorithm by exploiting the unique properties of signed networks. Based on the new proposed algorithm, we devise two optimization strategies to further improve the efficiency of the enumeration. We conduct extensive experiments on large real and synthetic datasets. The experimental results demonstrate the efficiency, effectiveness and scalability of our proposed algorithms.

Efficient Maximal Balanced Clique Enumeration in Signed Networks