Exponentially Twisted Sampling: a Unified Approach for Centrality Analysis in Attributed Networks

Cheng-Hsun Chang, Cheng-Shang Chang

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks and directed networks. The key idea of that framework is to sample a network by a symmetric and asymmetric bivariate distribution and then use that bivariate distribution to formerly defining various notions, including centrality, relative centrality, community, and modularity. The main objective of this paper is to extend the probabilistic definition to attributed networks, where sampling bivariate distributions by exponentially twisted sampling. Our main finding is that we find a way to deal with the sampling of the attributed network including signed network. By using the sampling method, we define the various centralities in attributed networks. The influence centralities and trust centralities correctly show that how to identify centralities in signed network. The advertisement-specific influence centralities also perfectly define centralities when the attributed networks that have node attribute. Experimental results on real-world dataset demonstrate the different centralities with changing the temperature. Further experiments are conducted to gain a deeper understanding of the importance of the temperature.

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