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arXiv · 1307.3768

Highly Dispersed Networks

Alan Gabel·P. L. Krapivsky·S. Redner
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Abstract

We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r, where r an increasing function of the degree of the ancestor. This mechanism leads to highly-dispersed networks with unusual properties: (i) existence of multiple macrohubs---nodes whose degree is a finite fraction of the total number of network nodes N, (ii) lack of self averaging, and (iii) anomalous scaling, in which N_k, the number of nodes of degree k scales as N_k N^{nu-1}/k^{nu}, with 1<nu<2.

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BibTeXRIS

Alan Gabel, P. L. Krapivsky, S. Redner. 2013-07-14. Highly Dispersed Networks. https://doi.org/10.1103/physreve.88.050802

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