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

Min-Yeong Kang (1) , Geoffroy C.B. Berthelot (2, 3, 4) , Christos Nicolaides (5, 6) , Jean-François Colonna (2) , Bernard Sapoval (1) , Denis S Grebenkov (1) , Liubov Tupikina (1, 7)

1 LPMC - Laboratoire de physique de la matière condensée
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 RELAIS - REsearch LAboratory for Interdisciplinary Studies
4 INSEP - Institut national du sport, de l'expertise et de la performance
5 UCY - University of Cyprus [Nicosia]
6 MIT Sloan - Sloan School of Management
7 CRI - Centre de Recherches Interdisciplinaires

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.

Domaines: Physique [physics]; Matière Condensée [cond-mat]; Mathématiques [math]; Physique mathématique [math-ph]

Min-Yeong Kang, Geoffroy C.B. Berthelot, Christos Nicolaides, Jean-François Colonna, Bernard Sapoval, et al.. Morphological organization of point-to-point transport in complex networks. Scientific Reports, 2019, 9, pp.8322. ⟨10.1038/s41598-019-44701-6⟩. ⟨hal-02149931⟩