Tests for Network Cascades via Branching Processes

We consider a network setting where branches form under the null of normal periods and larger branches form under the alternative. Our goal is to distinguish abnormally large branches, which we term cascades, from the common branches formed under the null. Call detail records provide the motivating example, as large call branches form after disruptive events, yet call branches also form during normal periods. We introduce a formal statistical testing framework to distinguish between branches formed under the null and alternative based on expected branch size. After defining the characteristics of edge formation under the null, we derive the expected size and variance of branches using the machinery of branching processes. We introduce a test statistic that compares observed average branch size to expected branch size under the null, which allows us to quantify the probability a cascade has occurred. Our test statistic is semiparametric, consistent, and asymptotically distributed standard normal under the null. Using call detail records from Yemen, we find a significant calling cascade occurred after the Presidential Palace was bombed in 2011. Lastly, we employ our statistic for event detection and successfully detect key violent events during the 2011 Yemeni Revolution.