Using cellular automata to model evolutionary dynamics of social network

Social networks usually serve as critical medium for information transmission, diffusion of epidemics, and spread of behaviour through sharing activities or similarities between individuals. A great interest in studying social influence and spread dynamics in social networks are witnessed recently. The related social network models are usually used for simulating and validating real social systems by using simulation data. But most of these social network models are built on existing nodes to study their edge statistical characteristics, such as degree distribution, clustering coefficient, community structure and etc., little consideration of evolutionary dynamics of social networks are involved, which are the physical base of various social networks and also an important research topic. In this paper, we consider one issue that what kind of factors is beneficial or harmful to the growth of nodes in a social network. Cellular automaton model is applied in this paper to attempt to study this issue, which can be seen as an evolutionary dynamics of a social network. Three kinds of factors named selfishness, reciprocity, and altruism, which are essential for constructing a social network, are introduced in the paper to analyse how they affect the growth of the virtual social network. A conclusion is obtained that reciprocity and altruism promote growth of nodes in the social network, on the other hand, selfishness inhibits the growth. We think it is interesting and significant to study this issue.