Rumor Spreading and Degree-Related Preference Mechanism on a Small-World Network

Zhi Zhu, Fengjian Liu, Dongsheng Liao

Humanities and Social Sciences School, National University of Defense Technology, Changsha, China.

DOI: 10.4236/sm.2012.24061                

Abstract

An alternate model for rumor spreading over small-world networks is suggested, of which two rumors (termed rumor 1 and rumor 2) have different nodes and probabilities of acceptance. The propagation is not symmetric in the sense that when deciding which rumor to adopt, high-degree nodes always consider rumor 1 first, and low-degree nodes always consider rumor 2 first. The model is a natural generalization of the well-known epidemic SIS model and reduces to it when some of the parameters of this model are zero. We find that rumor 1 (preferred by high-degree nodes) is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the NW small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it.

Keywords

Rumor; Degree-Related Preference Mechanism; Small-World Network

Conflicts of Interest

The authors declare no conflicts of interest.

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