Finiteness and Fluctuations in Growing Networks

Details Finiteness and Fluctuations in Growing Networks Finiteness and Fluctuations in Growing Networks

2002-07-03

arxiv.org/abs/cond-mat/0207107v2

J. Phys. A 35, 9517 (2002)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 5 figures, 2 column revtex format; minor revisions in response to referee comments, for publication in J. Phys. A

Scientific paper

10.1088/0305-4470/35/45/302

We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The resulting distributions exhibit an unusual finite-size scaling behavior and they are also sensitive to the initial conditions. We argue that fluctuations in the number of nodes of degree k become Gaussian for fixed degree as the size of the network diverges. We also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution.

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