A network provides powerful means of representing relationships between entities in complex physical, biological, cyber, and social systems. Any phenomena in those areas may be realized as changes in the structure of the associated networks. Hence, change detection in dynamic networks is an important problem in many areas, such as fraud detection, cyber intrusion detection, and health care monitoring. This article proposes a new methodology for monitoring dynamic networks for quick detection of structural changes in network streams and also estimating the location of the change-point. The proposed methodology utilizes the eigenvalues for the adjacency matrices of network snapshots and employs a nonparametric hypothesis to test if the distribution of the eigenvalues for the current snapshot is different from those of the previous ones along a sliding window of reference networks. The statistic of the nonparametric test, energy distance among eigenvalues, is monitored using a one-sided exponentially weighted moving average control chart. Then, after an anomaly detection signal from the monitoring scheme, eigenvalues for the snapshots are employed to calculate the energy statistic at various time steps to locate the change-point. The proposed method is intended to detect two types of structural changes in the networks: (1) change in the communication rates among individuals and (2) change in the community structure of the network. The proposed methodology is applied to both simulated and real-world data. Results indicate that the proposed methodology provides a reliable tool for monitoring networks streams and also estimating change-points locations for precise assessing of the networks under investigation.

中文翻译：

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一种社交网络中的非参数变化检测方法

网络提供了表示复杂物理、生物、网络和社会系统中实体之间关系的强大手段。这些领域中的任何现象都可以作为相关网络结构的变化来实现。因此，动态网络中的变化检测是许多领域的重要问题，例如欺诈检测、网络入侵检测和医疗保健监控。本文提出了一种监控动态网络的新方法，以快速检测网络流中的结构变化并估计变化点的位置。所提出的方法利用网络快照的邻接矩阵的特征值，并采用非参数假设来测试当前快照的特征值分布是否与沿着参考网络滑动窗口的先前特征值的分布不同。非参数检验的统计量，即特征值之间的能量距离，使用单边指数加权移动平均控制图进行监控。然后，在来自监控方案的异常检测信号之后，使用快照的特征值来计算不同时间步长的能量统计以定位变化点。所提出的方法旨在检测网络中两种类型的结构变化：（1）个体之间通信速率的变化和（2）网络社区结构的变化。所提出的方法适用于模拟和现实世界的数据。结果表明，所提出的方法提供了一种可靠的工具，用于监控网络流并估计变化点位置以精确评估所调查的网络。