Inferring Strange Behavior from Connectivity Pattern in Social Networks

Given a multimillion-node social network, how can we summarize connectivity pattern from the data, and how can we find unexpected user behavior? In this paper we study a complete graph from a large who-follows-whom network and spot lockstep behavior that large groups of followers connect to the same groups of followees. Our first contribution is that we study strange patterns on the adjacency matrix and in the spectral subspaces with respect to several flavors of lockstep. We discover that (a) the lockstep behavior on the graph shapes dense “block” in its adjacency matrix and creates “ray” in spectral subspaces, and (b) partially overlapping of the behavior shapes “staircase” in the matrix and creates “pearl” in the subspaces. The second contribution is that we provide a fast algorithm, using the discovery as a guide for practitioners, to detect users who offer the lockstep behavior. We demonstrate that our approach is effective on both synthetic and real data.