A Spectral Algorithm for Computing Social Balance

We consider social networks in which links are associated with a sign; a positive (negative) sign indicates friendship (animosity) between the connected nodes. Recent work studies such large online signed networks by applying theories that stem from the notion of social balance. Computing the social balance of a signed network requires counting the distinct configurations of the signed edges within all possible triangles that appear in the network. A naive algorithm for such counting would require time that is cubic to the total number of nodes; such an algorithm is infeasible for large signed networks that are generated from online applications. In this paper, we present an efficient spectral algorithm that computes approximate counts of the signed-triangle configurations. The essence of the algorithm lies in associating the eigenvalues of the adjacency matrix of a signed network with its signed-triangle configurations. Our experiments demonstrate that our algorithm introduces only a small error in the computed quantities while, at the same time, it achieves significant computational speedups.