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

Min-Yeong Kang; Geoffroy Berthelot; Liubov Tupikina; Christos Nicolaides; Jean-Francois Colonna; Bernard Sapoval; Denis S. Grebenkov

doi:10.1038/s41598-019-44701-6

arXiv · 1905.10333

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

Min-Yeong Kang·Geoffroy Berthelot·Liubov Tupikina·Christos Nicolaides·Jean-Francois Colonna·Bernard Sapoval·Denis S. Grebenkov

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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, Liubov Tupikina, Christos Nicolaides, Jean-Francois Colonna, Bernard Sapoval, Denis S. Grebenkov. 2019-05-24. Morphological organization of point-to-point transport in complex networks. https://doi.org/10.1038/s41598-019-44701-6

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