A new centrality measure for probabilistic diffusion in network

Kiyotaka Ide, Akira Namatame, Loganathan Ponnambalam, Fu Xiuju, Rick Siow Mong Goh

Abstract


Due to the significant increment of the volume of interactions among the population, probabilistic process on complex network can be often utilized to analyse diffusion phenomena in the society, then a number of researchers have studied especially from the perspectives of social network analysis, computer virus spread study, and epidemics study. So far, it has been believed that the largest eigenvalue and the principal eigenvector of the adjacency matrix can well approximate the dynamics on networks, but the accuracy of this approximation method has not study extensively. In our previous work, we found that not only the largest eigenvalue and the principle eigenvector but also the other eigenvalues and eigenvectors need to be considered when analysing the diffusion process on real networks. In this paper, we proposed a new centrality measure, the infection diffusion eigenvector centrality (IDEC), which considers all eigenvalues and eigenvectors. Our comparison results indicates that the IDEC shows better predictability than other centrality measures when the effective infection ratio is low, which will provide us with a good insight for practical application for developing the effective infection prevention methodology. Also, another interesting finding is that the eigenvector centrality shows poor predictability especially on the real networks. In addition, we conduct the recovery probability enforcement simulation, which highlights the advantage of IDEC for the range below the critical point.

Keywords


Infection; SIS model; Complex network; Centrality; Eigenvalue; Eigenvector

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