Log-Networks

Details Log-Networks Log-Networks

2004-10-14

arxiv.org/abs/cond-mat/0410379v3

Phys. Rev. E 71, 036118 (2005)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 6 figures, 2-column revtex4 format. Version 2: minor changes in response to referee comments and to another proofread

Scientific paper

10.1103/PhysRevE.71.036118

We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such as the size dependence of the number of links and the in- and out-degree distributions. We also compare our predictions with real networks where the node degree also grows slowly with time -- the Internet and the citation network of all Physical Review papers.

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