多重边融合复杂网络动态演化模型

Dynamic Evolution Model of United Complex Networks with Multi-Links

针对多个性质不同、相互融合的复杂网络演化过程时变非均衡,网络结构层级交织,特点规律难以测度的问题,提出了一个多重边融合复杂网络动态演化模型。首先,定义多重边融合复杂网络的相关概念,分析融合关系与层级关系的转化过程,按照节点、边性质的差异,拆分融合节点和重合边,将多重边融合复杂网络转化成交织型层级复杂网络;其次,定义节点的度值饱和度和吸引因子,提出交织型层级复杂网络的演化算法和局域世界演化模型,讨论了4种典型的节点演化情形,运用平均场方法分析了模型演化的度分布规律;最后进行了数值仿真分析,结果表明,演化过程结束后,未达到饱和状态的节点度值服从指数分布且误差不超过6%,已达到饱和状态的节点度值服从其连接容量的分布规律且误差不超过3%,网络交织系数与最高的新增节点概率、初始边数呈正相关性。研究结果验证了模型的可行性和有效性,为探索多重边融合复杂网络演化过程与规律提供了新的思路和方法,在交通网、通信网、社交网等结构与动力学研究方面具有良好的应用前景。

Aiming at the problem that during the evolution process of interconnected complex networks, there exist nonuniform time-varying property and layered interlaced network structure, leading to the difficulty in measuring their characteristics and rules, a dynamic evolution model of united complex network with multi-links （MLUCN） is proposed. Firstly, we define some related concepts of MLUCN, analyze the conversion process of fusion and hierarchy relationship, and split fusion nodes and overlapped edges according to the property differenee between nodes and edges, then the MLUCN is transformed to interlaced layered complex networks （ILCN）. Secondly, the node degree saturation and attraction factor are defined. The evolution algorithm and local-world evolution model for ILCN are put forward, and four situations of node evolution are discussed. The mean field method is used to analyze the degree distribution rule during evolution. Finally, numerical simulation is performed. The results show that the node degree not reaching saturation obeys the exponential distribution with an error no more than 6 %; the node degree reaching saturation obeys their eonneetion capacities＇ distribution with an error no more than 3 %; the network weaving coefficients have a positive correlation with the highest probability of new node and the initial number of connected edges. The resultsverified the feasibility and effectiveness of the proposed model. This model provides a new idea and method for exploring MLUCN evolution process and rule, and also has good application prospects in the structure and dynamics researches of transportation network, communication network and social network, etc.