Random walk on signed networks

Random walks on the traditional networks have achieved a series of research results in many aspects, such as analysis of node centrality, community detection, link prediction, etc. and have a wide range of applications. Actually, random walks can also apply to the signed networks which contain two types of links: positive links and negative links. However, there are few related researches about random walks on signed networks. And also we find that most researches about random walks on signed networks assume that the agent walks only along the positive links in the diffusion process, which loses the effective information of negative links. So in this paper, we propose a signed random walk model which allows that the random walker walks along the negative links with a smaller probability than positive links. We focus on two aspects of the signed random walk as follows: (1) the convergence of transition probability matrix. (2) the application to community detection in signed networks. And we apply the signed random walk to both artificial signed networks and real-world signed networks. The results show that the position and density of negative links in the signed network will affect the convergence rate of transition probability matrix. We also find that the signed random walk can be used to uncover the meaningful community structures in the signed networks.