Tree Networks with Causal Structure

Details Tree Networks with Causal Structure Tree Networks with Causal Structure

2002-11-23

arxiv.org/abs/cond-mat/0211527v4

Phys. Rev. E 67, 066106 (2003)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 2-column revtex format, 1 eps figure, misprints corrected

Scientific paper

10.1103/PhysRevE.67.066106

Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree graphs, an analytically solvable case. General formulae are derived, describing the degree distribution, the ancestor-descendant correlation and the probability a randomly chosen node lives at a given geodesic distance from the root. It is shown that the Hausdorff dimension $d_H$ of the causal networks is generically infinite, in contrast to the maximally random trees, where it is generically finite.

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