An observation of power law distribution in dynamic networks

Network dynamics has become a popular area of study because of the evolutionary and adaptive nature of networks over time. Therefore, abnormal change detection is critical to the understanding and control of network dynamics. This paper presents differences in graph diameter as a method for detecting abnormal changes in a network time series. A formal definition of graph diameter is presented, as are theoretical implications, examples and computational results. An apparent means for characterization of network state without dependence on other networks in the time series is presented, which is also based on the network diameter. This leads directly to the ability to identify anomalous change and to characterize the effects on the network communications. The power law distribution of this diameter characterization demonstrates network susceptibility and leads to a better understanding of the network behavior.