Wu Zhenhua, Braunstein Lidia A, Havlin Shlomo, Stanley H Eugene
Center for Polymer Studies, Boston University, Boston, MA 02215, USA.
Phys Rev Lett. 2006 Apr 14;96(14):148702. doi: 10.1103/PhysRevLett.96.148702. Epub 2006 Apr 13.
Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly different transport properties, characterized by centrality--the number of times a node (or link) is used by transport paths. One component, superhighways, is the infinite incipient percolation cluster, for which we find that nodes (or links) with high centrality dominate. For the other component, roads, which includes the remaining nodes, low centrality nodes dominate. We find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law, with an exponent smaller than that for the entire MST. The significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network, the superhighways.
加权网络中的传输由最小生成树（MST）主导，即连接所有节点且总权重最小的树。我们发现，最小生成树可分为两个截然不同的部分，它们具有显著不同的传输特性，以中心性来表征——节点（或链路）被传输路径使用的次数。其中一个部分是超级高速公路，它是无限初渗集群，我们发现具有高中心性的节点（或链路）在其中占主导地位。对于另一个部分，即包含其余节点的道路，低中心性节点占主导地位。我们还发现，无限初渗集群的中心性分布满足幂律，其指数小于整个最小生成树的指数。这一发现的意义在于，通过改善网络中极小的一部分，即超级高速公路，就能显著提高全局传输效率。
