度关联无标度网络上的有倾向随机行走∗

摘要

Random walk has been applied to exploring the effective transport strategy of data package in complex networks. Because the disassortative degree correlation is ubiquitous in technical networks including the internet, we study the biased random walks in the scale-free networks with the disassortative degree correlation. Computer simulation shows that the degree correlation changes the behavior of the random walk. Random walkers are located on small degree nodes with a low probability, and they can be distributed homogeneously on other nodes. We find out the optimal biased coefficient that ensures the most homogeneous distribution on large nodes. In the optimal case, the degree-correlated network exhibits a more efficient random walk than degree-uncorrelated networks. We propose the mechanism for the effect of the disassortative mixing on the random walk.%有倾向随机行走是研究网络上数据包路由策略的有效方法。由于许多真实技术网络包括互联网都具有负的度关联特征，因此本文研究这种网络上的有倾向随机行走性质。研究表明：在负关联网络上粒子可以在连接度较大的节点上均匀分布，而连接度小的节点上粒子较少；负关联网络上随机行走的速度比非关联网络更快；找到了负关联网络上的最佳倾向性系数，在此情况下负关联网络上随机行走的速度远快于非关联网络。负关联网络既可以利用度小的节点容纳粒子，又可以利用度大的节点快速传输，这是负关联网络上高行走效率产生的机制。