Properties of a random attachment growing network

Details Properties of a random attachment growing network Properties of a random attachment growing network

2003-05-13

arxiv.org/abs/cond-mat/0305299v2

Physical Review E 68 066104 (2003)

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 19 pages, 6 figures. Discussion section, comments, a new figure and a new reference are added. Equations simplified

Scientific paper

10.1103/PhysRevE.68.066104

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing network and joins them with probability delta by undirected edges. The 'activity' of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of delta, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k=1. There is no giant component formed for any delta and thus in this sense there is no phase transition. However, the average component size diverges for delta greater or equal than one half.

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