Inhomogeneous substructures hidden in random networks

Details Inhomogeneous substructures hidden in random networks Inhomogeneous substructures hidden in random networks

2006-03-20

arxiv.org/abs/cond-mat/0603515v1

Phys. Rev. E 73, 037102 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.73.037102

We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths through the edge. We find that the LSTs present very inhomogeneous structures in contrast to the homogeneous structures of the original networks. Moreover, it turns out that the structure of the LST changes dramatically as the edge density of an ER network increases, from scale free with a cutoff, scale free, to a starlike topology. These would not be possible if the weights are randomly distributed, which implies that topology of the shortest path is correlated in spite of the homogeneous topology of the random network.

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