Causal and homogeneous networks

Details Causal and homogeneous networks Causal and homogeneous networks

2005-03-22

arxiv.org/abs/cond-mat/0503548v3

AIP Conf. Proc. 776, 14 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

short review submitted to AIP proceedings, CNET2004 conference; changes in the discussion of the distance distribution for gro

Scientific paper

10.1063/1.1985374

Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for corresponding homogeneous networks. We explain the origin of this effect and illustrate it using as an example a solvable model of random trees. We also discuss the issue of stability of the scale-free node degree distribution. We show that a surplus of links may lead to the emergence of a singular node with the degree proportional to the total number of links. This effect is closely related to the backgammon condensation known from the balls-in-boxes model.

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