Partition of the minimum spanning tree into superhighways and roads
Abstract
For random, scale-free and lattice networks we study the minimum spanning tree (MST), defined to be the tree, out of all possible spanning trees with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly different transport properties characterized by the ``betweenness centrality'' (BC). One component, the {\it superhighways}, is the infinite incipient percolation cluster (IIC); for the superhighways, we find that nodes (or links) with high BC dominate. The other component, {\it roads}, includes the remaining nodes (or links) excluding the IIC; for the roads, we find that low BC dominates. We find that the distribution of BC for the IIC satisfies a power law, with exponent different (smaller) than that for the entire MST.Keywords
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