Correlation effects on topological structure in complex network evolution

Network growth model is an important and popular research topic aimed at uncovering the mechanisms of network formation and evolution. Most growth models focus on two key mechanisms: growth and preferential attachment without directly accounting for the correlation effects, existing in many realistic network systems. Here, we propose a preferential correlation growth model by introducing a proximity parameter that controls the proximity between nodes connected to newly added nodes. The smaller the proximity parameter, the shorter the distance between the selected nodes, and the stronger the correlation between them. When the proximity parameter approaches infinity, our model reduces to the BA model. By comparing simulations with different proximity parameter, we find that a high degree of correlation significantly enhances the robustness, both local and global efficiency of the network. Besides, our model demonstrates high clustering coefficient, short average path length, and richer cyclic structures, which are closer to real-world networks. Furthermore, our network model effectively addresses the low clustering coefficient issue of the BA model and provides a better understanding of the cyclic structures in real-world networks. Specially, we find that on the mesoscopic time scale, the correlation effects can significantly improve thermodynamic efficiency from a statistical perspective. Our work shows that correlation should be another key mechanism of network formation in addition to the preferential attachment, deserved to be considered for better understanding of the structure and function of the network.