摘要:
本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足pijα dij^-α （α≥ 0）,其中dij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN（c≥ 0）的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α0 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α0单调增加,并趋近最优值1.5.
Abstract:
In this paper, we construct a cost constrained spatial network by adding long-range connections to the one-dimensional circle. The probability for a long-range connection between nodes i and j is pijα dij^-α （α≥ 0）, where dij is the lattice distance and the total length of the long-range connections is set to be ∧=cN（c≥ 0）, where c is a positive constant and N is the network size. According to the simulation and numeric results, we find an optimal power-law exponent α0 such that the mean first-passage time is shortest. Furthermore, the shortest mean first-passage time has the power law relationships with the network size N. With the increase of network size N and the total cost ∧, the optimal power-law exponent α0 increases monotonically and approaches 1.5.
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