New Discovery of the Emergence Mechanism of High Clustering Coefficients

Abstract

In our statistical analysis, we have discovered that the distance distribution (referring to Euclidean distance) of many real networks follows certain patterns, especially the distances between connected nodes obey a scale-free distribution. However, the classic BA model does not exhibit this characteristic. Furthermore, existing network models are mostly evolved based on degree-preference mechanisms, without considering the potential influence of factors such as edge weights like spatial geographical factors on node-edge connections in real networks. Taking distance-weighted preferences as an example, this study proposes a network evolution model based on distance preference connections as the fundamental mechanism. By applying probability theory and mean-field theory, the model’s degree distribution is calculated to be exponential, with a clustering coefficient greater than that of the BA model and consistent with data from some real networks. Our model reveals that this distance preference mechanism may be the fundamental mechanism underlying the emergence of high clustering in real networks. Additionally, by incorporating degree-preference connection mechanisms, the model is further analyzed and improved to better match actual network evolution behaviors. The research results provide a possible explanation for resolving the controversy surrounding the scale-free nature of networks.