Evolutionary dynamics analysis of complex network with fusion nodes and overlap edges

Multiple complex networks, each with different pro-perties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are diffi-cult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges (CNF-NOEs) is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion rela-tionship and hierarchy relationship. According to the property dif-ference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is trans-formed to interlacing layered complex networks (ILCN). Secondly, the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method. Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distri-bution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE's evolving process and law. Also, the model has good application prospects in structure and dynamics research of trans-portation network, communication network, social contact network, etc.