  Sequential change-point detection for graphs is a fundamental problem for
streaming network data types and has wide applications in social networks and
power systems. Given fixed vertices and a sequence of random graphs, the
objective is to detect the change-point where the underlying distribution of
the random graph changes. In particular, we focus on the local change that only
affects a subgraph. We adopt the classical Erdos-Renyi model and revisit the
generalized likelihood ratio (GLR) detection procedure. The scan statistic is
computed by sequentially estimating the most-likely subgraph where the change
happens. We provide theoretical analysis for the asymptotic optimality of the
proposed procedure based on the GLR framework. We demonstrate the efficiency of
our detection algorithm using simulations.
