Densification and structural transitions in networks that grow by node copying

U. Bhat, P. L. Krapivsky, R. Lambiotte, S. Redner

Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs


We introduce a growing network model, the copying model, in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability p. When p<12, this algorithm generates sparse networks, in which the average node degree is finite. A power-law degree distribution also arises, with a nonuniversal exponent whose value is determined by a transcendental equation in p. In the sparse regime, the network is "normal," e.g., the relative fluctuations in the number of links are asymptotically negligible. For p≥12, the emergent networks are dense (the average degree increases with the number of nodes N), and they exhibit intriguing structural behaviors. In particular, the N dependence of the number of m cliques (complete subgraphs of m nodes) undergoes m-1 transitions from normal to progressively more anomalous behavior at an m-dependent critical values of p. Different realizations of the network, which start from the same initial state, exhibit macroscopic fluctuations in the thermodynamic limit: absence of self-averaging. When linking to second neighbors of the target node can occur, the number of links asymptotically grows as N2 as N→∞, so that the network is effectively complete as N→∞.

langue originaleAnglais
Numéro d'article062302
journalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Numéro de publication6
Les DOIs
Etat de la publicationPublié - 8 déc. 2016

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