Network reconstruction by the stationary distribution of random walk process

TL;DR

This paper presents a method to reconstruct network structures using only the stationary distribution of a random walk, accurately inferring links, degree sequences, and total links without needing evolution data.

Contribution

The proposed method reconstructs network topology solely from stationary distribution data, including total links and degree sequence, without requiring additional dynamic information.

Findings

Accurately reconstructs networks from stationary distribution.

Works on both model and real-world networks.

Effective even with approximate stationary distributions.

Abstract

It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk process can only reflect the relative size of node degrees directly, how to infer the real connection is still a problem. In this paper, we will propose a method to reconstruct network by the random walk process, which can reconstruct the total number of links, degree sequence and links sequentially. In our method, only the stationary distribution is used, and no data of the evolution process is needed, such as the first passage time. We perform our method on some network models and real-world network, the results indicate our method can reconstruct networks accurately, even when we can not get the exact stationary distribution.