Finding large balanced subgraphs in signed networks Bruno Ordozgoiti Antonis Matakos Aristides Gionis∗ Aalto University Aalto University KTH Royal Institute of Technology
[email protected] [email protected] [email protected] ABSTRACT Signed networks are graphs whose edges are labelled with either a + + - - + + - - positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The + + - - concept of balance in signed graph theory determines whether a network can be partitioned into two perfectly opposing subsets, and Figure 1: The four possible signed triangles. The two on the is therefore useful for modelling phenomena such as the existence left are balanced, while the two on the right are not. of polarized communities in social networks. While determining whether a graph is balanced is easy, finding a large balanced sub- Many social-media platforms can be represented by graphs. Thus, graph is hard. The few heuristics available in the literature for this graph theory has found a variety of applications in this domain purpose are either ineffective or non-scalable. In this paper we over the last few decades, such as community detection [13], parti- propose an efficient algorithm for finding large balanced subgraphs tioning [4], and recommendation [30]. One limitation of the graph in signed networks. The algorithm relies on signed spectral theory representations usually employed in the literature is that they can and a novel bound for perturbations of the graph Laplacian. In capture the existence, or even the strength, of connections between a wide variety of experiments on real-world data we show that vertices, but not their disposition.