基于拓扑路径的网络演化传播机制研究

Study of Propagation Mechanism in Networks Based on Topological Path

现有的社会网络信息传播模型主要分析传播的途径,将传播过程与节点的度相结合,而传播媒介常常被忽略。在现实世界的网络中,传播源作为一个物理传播媒介通常由特定的路径从一个节点传播到另一个节点(基于路径的传播)。本研究不再局限于节点的总体行为分析,而是分别考虑每个节点的状态转换,用连续状态的马尔科夫链分析来模拟传播源和路径对传播行为的影响。该方法通过引入平均场近似,将基于路径的传播机制的计算复杂度从指数级别降低到多项式级别;定义了同时包含路由选择和交通信息的传播特性矩阵,并得出了基于路径传播的关键传播阈值。当有效传播率低于关键传播阈值时,传播就会逐渐消亡,因此可以运用该关键传播阈值来促进或抑制基于路径的传播。最后,除了随机无标度网络,引入了现实世界网络交通作为研究案例来对比基于连接和基于路径的传播行为,结论表明所提模型在社交网络中的传播具有高度持续性和极强的稳定性。

The existing information dissemination model of social network mainly analyzes the ways of dissemination,and combines the process of communication with the degree of nodes.However,the media is often ignored.In real-world networks,the propagation source,a physical propagation medium,usually propagates from one node to another via a specific path.This paper was no longer limited to analyze the overall behavior of nodes,but considered each node separately,and used the continuous Markov chain to simulate the influence of propagation sources and paths on propagation.By introducing a mean field approximation,the computational complexity of the path-based pro-pagation is reduced from an exponential level to a polynomial level.This paper also defined a propagation characteristic matrix containing both routing and traffic information,and derived a key propagation threshold based on path propagation.When the effective transmission rate is below the threshold,the propagation will gradually die out,so we can use this critical propagation threshold to promote or suppress path-based propagation.Finally,in addition to the stochastic scale-free network,this paper introduced the real-world network traffic as a research case to compare the connection-based and path-based propagation behaviors.The conclusions show that the model’s propagation in social networks is highly persistent and extremely stable.