We present new algorithms for detecting the emergence of a community in large networks from sequential observations. The networks are modeled using Erdos-Renyi random graphs with edges forming between nodes in the community with higher probability. Based on statistical changepoint detection methodology, we develop three algorithms: the Exhaustive Search (ES), the mixture, and the Hierarchical Mixture (H-Mix) methods. Performance of these methods is evaluated by the average run length (ARL), which captures the frequency of false alarms, and the detection delay. Numerical comparisons show that the ES method performs the best; however, it is exponentially complex. The mixture method is polynomially complex by exploiting the fact that the size of the community is typically small in a large network. However, it may react to a group of active edges that do not form a community. This issue is resolved by the H-Mix method, which is based on a dendrogram decomposition of the network. We present an asymptotic analytical expression for ARL of the mixture method when the threshold is large. Numerical simulation verifies that our approximation is accurate even in the non-asymptotic regime. Hence, it can be used to determine a desired threshold efficiently. Finally, numerical examples show that the mixture and the H-Mix methods can both detect a community quickly with a lower complexity than the ES method.

本文提出了基于Erdos-Renyi随机图的新算法，用于从时序观测中检测网络中社区的出现。 所开发的三个算法分别为Exhaustive Search（ES），mixture，和Hierarchical Mixture（H-Mix）。 数值比较显示H-Mix方法是性能最好的方法，与ES方法相比，H-Mix方法具有更低的计算复杂度。

在线社区识别的顺序变点方法