A topological evolution model based on the attraction of the motif vertex

As a fundamental problem in the field of the network science, the study of topological evolution model is of great significance for revealing the inherent dynamics and mechanisms of complex network evolution. In order to study the influence of different scales of preferential attachment on topological evolution, a topological evolution model based on the attraction of the motif vertex is proposed. From the perspective of network motif, this model proposes the concept of attraction of the motif vertex based on the degree of the motif, quantifies the influence of local structure on the node preferential attachment, and performs the preferential selection of the new link based on the Local World model. The simulation experiments show that the model has the small world characteristic apparently, and the clustering coefficient varies with the scale of the local world. The degree distribution of the model changes from power-law distribution to exponential distribution with the change of parameters. In some cases, the piecewise power-law distribution is presented. In addition, the proposed model can present a network with different matching patterns as the parameters change.