Characterization&Modeling Of Possible Internal Factors Affecting The Evolutionary Path And Formation Of Network Motif During The Evolution Of Complex Network

In this paper, we propose a new model for network evolution. The model, which is based on Evolutionary Algorithm (EA), combines Modularly Vary-ing Goals and Game Theory to describe the possible external and internal factors during the evolution. Specifically, Modularly Varying Goals can cap-ture the changing environment and different Game theory strategies can cha-racterize different"rational behaviors"of individuals within the network. The purpose of these behaviors is to maximize the benefits of nodes in network. Obviously, our model is better than other network evolution models based on EA. As we know, EA can gradually improve fitness of the whole population, but it can not guarantee the maximum benefits of nodes. Thus, the evolutio-nary models totally based on EA have limitations, for they all ignore the dy-namic behaviors of nodes. However, our model incorporates these behaviors during network evolution.Through introducing different game theory strategies into our model, we perform two independent simulations of network evolution. Moreover, the statistically quantitative measurement Z-score is used to measure the fre-quency of network motifs. Comparing Z-scores of different network motifs, we find that competitions may speed up the evolutionary process. Meanwhile, competitions between nodes can promote the formation of some network mo-tifs and suppress the formation of some other network motifs.During network evolution, the internal factors (game theory strategies that nodes of network adopt) have great effects on the formation of network motifs. Different game theory strategies can promote different network motifs.