Universal evolution patterns of degree assortativity in social networks

Degree assortativity characterizes the propensity for large-degree nodes to connect to other large-degree nodes and low-degree to low-degree. It is important to describe the forces forming the network and to predict the behavior of dynamic systems on the network. To understand the evolutionary dynamics of degree assortativity, we collect a variety of empirical temporal social networks, and find that there is a universal pattern that the degree assortativity increases at the beginning of evolution and then decreases to a long-lasting stable level. We develop a bidirectional selection model to re-construct the evolution dynamic. In our model, we assume each individual has a social status that—in analogy to Pareto’s wealth distribution —follows a power-law distribution. We assume the social status determines the probability of an interaction between two actors. By varying the ratio of link establishment from within the same status level to across different status levels, the simulated network can be tuned to be assortative or disassortative. This suggests that the rise-and-fall pattern of degree assortativity is a consequence of the different network-forming forces active at different mixing of status. Our simulations indicate that Pareto social status distribution in the population may drive the social evolution in a way of self-optimization to promote the social interaction among individuals and the status gap plays an important role for the assortativity of the social network.