Abstract
The problem of sending the maximum amount of flow q between two arbitrary nodes s and t of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between s and t. The average of q over all node pairs with smaller degree kmin is ⟨q⟩kmin ≃ c kmin for large kmin with c a constant implying that the statistics of q is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and q can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient c. The applicability of our results to real-world networks is tested for the Internet at the autonomous system level.
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