Flows on Graphs with Random Capacities

Details Flows on Graphs with Random Capacities Flows on Graphs with Random Capacities

2006-09-06

arxiv.org/abs/cond-mat/0609145v1

Physical Review E 74, 051110 (2006)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 6 figures

Scientific paper

10.1103/PhysRevE.74.051110

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.

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