Morphological organization of point-to-point transport in complex networks

Abstract : We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. the random choice of two nodes, a source and a drain, to which a potential difference is applied, selects two tree-like structures, one emerging from the source and the other converging to the drain. these trees merge into a large cluster of the remaining nodes that is found to be quasi-equipotential and thus presents almost no resistance to transport. such a global "tree-cluster-tree" structure is universal and leads to a power law decay of the currents distribution. Its exponent, −2, is determined by the multiplicative decrease of currents at successive branching points of a tree and is found to be independent of the network connectivity degree and resistance distribution.
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Min-Yeong Kang, Geoffroy Berthelot, Christos Nicolaides, Jean-François Colonna, Bernard Sapoval, et al.. Morphological organization of point-to-point transport in complex networks. Scientific Reports, Nature Publishing Group, 2019, 9, pp.8322. ⟨10.1038/s41598-019-44701-6⟩. ⟨hal-02149931⟩

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