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Detection and Diagnosis of Distribution Changes of Degree Ratio in Complex Networks

The detection and diagnosis problems of distribution changes of degree ratio in complex networks are studied in this paper. We not only give the asymptotic expressions of the in-control and out-of-control average run lengths in detecting the distribution change by the cumulative sum chart, but also provide an effective and practicable method to transform the detection problem of the high dimensional Markov chain into a one-dimensional problem. Moreover, three multi-charts each based on the reference transition probabilities, the principal components, and the entropy statistics are presented to deal with the diagnosis problem. Finally, a real financial network which describes the dynamics and random correlations among 90 assets is investigated to demonstrate the detection and diagnosis performance of both the reference-free Cuscore chart and the multi-chart based on the entropy statistics.