Anomaly Graphs and Champions

A scan statistic methodology for detecting anomalies has been developed for application to graphs. We equate anomalies with vertices that exhibit high local connectivity properties. In particular we look for cases where all vertices have similar local connectivity, except for one vertex (a champion) that has much higher connectivity at a certain level. For example, a neighborhood champion is a vertex whose closed neighborhood is larger than those of other vertices; a scale k champion is a vertex whose distance k closed neighborhood is larger than those of other vertices. An anomaly graph is a graph with a scale k champion, in which all neighborhoods are the same size at distance h when h < k, and the distance k closed neighborhoods of the non-champions are of equal size. We shall survey the constructions of anomaly graphs and more general results on neighborhood champions.