Edge-based stochastic network model reveals structural complexity of edges

Abstract

Abstract Network Science defines complex systems as objects interacting in a network with nodes and edges. Stochastic network models that treat networks as a collection of nodes with fixed degree distributions and randomly-connected edges have provided significant theoretical support for network analyses. However, the structural characteristics of edges in complex networks remain largely unknown due to the lack of edge-based network models. Here, we propose a general edge-based stochastic network model with constrained edge-degree distributions and arbitrary node-degree distributions. The random edge configuration method is used to build the model with the explicit edge-connected probability, which can also be explained by Laplacian dynamics. The model reveals both basic and complex structural characteristics of edges in networks, including statistical structural characteristics, link community structure, and higher-order organization. The experimental results show the advantageous performance on both link community and motifs detection based on the edge-based stochastic network model, which demonstrate that the model is useful for conducting quantitative comparisons the complex structural characteristics of edges. The edge-based stochastic network model is fundamental model to help understand the complex structure of edges that is hard to quantify in the complex networks.