Path finding strategies in scale-free networks

Details Path finding strategies in scale-free networks Path finding strategies in scale-free networks

2001-11-13

arxiv.org/abs/cond-mat/0111232v2

Phys. Rev. E 65, 027103 (2002).

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, final form

Scientific paper

10.1103/PhysRevE.65.027103

We numerically investigate the scale-free network model of Barab{\'a}si and Albert [A. L. Barab{\'a}si and R. Albert, Science {\bf 286}, 509 (1999)] through the use of various path finding strategies. In real networks, global network information is not accessible to each vertex, and the actual path connecting two vertices can sometimes be much longer than the shortest one. A generalized diameter depending on the actual path finding strategy is introduced, and a simple strategy, which utilizes only local information on the connectivity, is suggested and shown to yield small-world behavior: the diameter $D$ of the network increases logarithmically with the network size $N$, the same as is found with global strategy. If paths are sought at random, $D \sim N^{0.5}$ is found.

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