Testing Cluster Properties of Signed Graphs

This work initiates the study of property testing in signed graphs, where every edge has either a positive or a negative sign. We show that there exist sublinear query and time algorithms for testing three key properties of signed graphs: balance (or 2-clusterability), clusterability and signed triangle freeness. We consider both the dense graph model, where one queries the adjacency matrix entries of a signed graph, and the bounded-degree model, where one queries for the neighbors of a node and the sign of the connecting edge. Our algorithms use a variety of tools from unsigned graph property testing, as well as reductions from one setting to the other. Our main technical contribution is a sublinear algorithm for testing clusterability in the bounded-degree model. This contrasts with the property of k-clusterability in unsigned graphs, which is not testable with a sublinear number of queries in the bounded-degree model. We experimentally evaluate the complexity and usefulness of several of our testers on real-life and synthetic datasets.