Cluster Expansion Analysis for Dynamic Networks

Motifs, which are subgraphs that recur regularly, can be used to effectively describe the structure of networks. Using statistical mechanics to investigate the distribution of subgraphs is one way to learn about a network’s motif structure. We use the cluster expansion from statistical physics to address the use of motifs as network primitives in this paper. We derive the partition function for a network by mapping network motifs to clusters in the gas model, which helps us to measure global thermodynamic quantities including energy and entropy. We present analytical expressions for the number of different types of motifs, as well as the entropy associated with them. We test the qualitative and quantitative characterizations of the motif entropy derived from the partition function using numerical experiments on synthetic and real-world data sets. The motif entropy for real-world networks, such as financial stock market networks, is vulnerable to network structure variance, according to our findings. This is consistent with recent findings that network motifs are fundamental elements with well-defined information-processing functions. Our model can detect sudden changes in network structure and differentiate between different types of time-dependency for different types of anomalies.

Author (s) Details

Jianjia Wang
School of Computer Engineering and Science, Shanghai University, Shanghai, P.R. China and Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, P. R. China.

Zhihong Zhang
School of Informatics, Xiamen University, Xiamen, Fujian, China.

Dongdong Chen
School of Informatics, Xiamen University, Xiamen, Fujian, China.

Edwin R. Hancock
University of York, York, UK.

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