Monitoring Network Streams based on Eigenvalues of Adjacency Matrix

Network analysis is a fundamental tool for studying various systems in the social, biological, and engineering domains. A new surveillance plan is proposed in this paper to monitor network streams. The proposed plan constructs a statistic based on the Eigen values of a baseline adjacency matrix. The baseline adjacency matrix is defined using a likelihood-ratio test on the in-degree and out-degree of the individuals in the network. The proposed plan is applied to both simulated and real networks, and achieved Run Lengths are analyzed. For the simulated networks, results indicate that the proposed plan outperforms the existing surveillance plans and is capable of detecting both local and global anomalies. The proposed plan is also employed to monitor the contracting network of Tehran Municipality as a real world network. Results reveal that the roposed plan is also applicable to detect anomalies in real world networks.

Keywords:

Social Network Monitoring , Baseline Adjacency Matrix , Eigen Values , Likelihood-ratio Test