Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
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webmaster@bioinf.uni-leipzig.de
) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:webmaster@bioinf.uni-leipzig.de
©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
Statistics of cycles in large networks
Konstantin Klemm, Peter F. Stadler
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Status: Published
Phy.Rev.E, 73: 025101 (2006)
Abstract
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.