Statistics of cycles in large networks

Details Statistics of cycles in large networks Statistics of cycles in large networks

2005-06-20

arxiv.org/abs/cond-mat/0506493v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures

Scientific paper

We present a Markov Chain Monte Carlo method for sampling cycle length in large graphs. Cycles are treated as microstates of a system with many degrees of freedom. Cycle length corresponds to energy such that the length histogram is obtained as the density of states from Metropolis sampling. In many growing networks, mean cycle length increases algebraically with system size. The cycle exponent $\alpha$ is characteristic of the local growth rules and not determined by the degree exponent $\gamma$. For example, $\alpha=0.76(4)$ for the Internet at the Autonomous Systems level.

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