Applying correlation dimension to the analysis of the evolution of network structure

Abstract We propose a network model that includes some critical events. These critical events correspond to drastic changes in the structure. Here, the correlation dimension is found to be able to globally characterize changes in the network structure. Based on the model, we find a relationship between the stability of the network structure and the dimension. The structural evolution of the network is divided into different phases, with corresponding critical events between the different phases. If the network changes less in the same phase, the resulting Jaccard distance matrix has a smaller dimension. We also validated the conclusions based on the model with real data. We use stock data to construct some threshold networks, and find that the dimension of the surrogate time series is larger than the dimension based on the original data. This implies that changes in the network structure are not fully extracted by the one factor model. Finally, by comparing with the network model based on Erdos-Renyi random graph, we find that the correlation dimension can be used to capture the hidden temporal features in the network set.

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