A simple model to characterize social networks

Abstract

For the purpose of prediction analysis of customer relationships in social networks, this paper proposes a simple model that can generate future states of a social network based on relevant data analysis. In this model, nodes and edges of the social network are inserted at the same preferential attachment probabilities, but deleted at different anti-preferential attachment probabilities. In this model, we consider the limit of the network size, the directions of incident links and the factor of time in attractiveness when deleting nodes. Networks generated from this model have a nice property that the degree distribution follows the power-law, which desirably characterizes an essential property of social networks. This property is derived by applying the mean-field theory [7]. It is validated through simulation: we use C++, MATLAB to generate the degree distribution map of our model, and PAJEK to draw the topology map of social networks that was generated by our model. We also show that networks generated from our model can self-organize into scale-free networks. If -C - 1<; E <; m-2C/2, deleting nodes will not result in destruction of the network