时序网络演化速度对传播的影响分析

Effects analysis of network evolution speed on propagation in temporal networks

为分析时序网络演化速度对传播过程的影响,通过改进已有的时序相关系数定义,给出了一个网络演化速度指标;同时,提出了一个具有非马尔可夫性质的时序网络演化模型。在每个时间步,每一个给定的激活节点都以概率r在网络中随机选择一个节点,以概率1-r在该激活节点的原邻居中随机选择一个节点,并在该激活节点与所选节点间建立连边。模拟结果表明:网络模型参数r与网络演化速度指标之间有单调增的关系;同时,激活节点随机连边的概率r越大,网络传播范围就越广。由此可知:演化速度快的时序网络有利于网络传播;进一步地,网络拓扑结构的快速变化有利于信息的快速传播,但不利于抑制病毒传播。

An index of network evolution speed and a network evolution model were put forward to analyze the effects of network evolution speed on propagation. The definition of temporal correlation coefficient was modified to characterize the speed of the network evolution; meanwhile, a non-Markov model of temporal networks was proposed. For every active node at a time step, a random node from network was selected with probability r, while a random node from former neighbors of the active node was selected with probability 1- r. Edges were created between the active node and its corresponding selected nodes. The simulation results confirm that there is a monotone increasing relationship between the network model parameter r and the network evolution speed; meanwhile, the greater the value of r, the greater the scope of the spread on network becomes. These mean that the temporal networks with high evolution speed are conducive to the spread on networks. More specifically, the rapidly changing network topology is conducive to the rapid spread of information, but not conducive to the suppression of virus propagation.