Extremum statistics in scale-free network models

Details Extremum statistics in scale-free network models Extremum statistics in scale-free network models

2002-05-20

arxiv.org/abs/cond-mat/0205411v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

We investigate the statistics of the most connected nodes in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation--due to the finite size of the network--of the degree distribution governs the scaling of the extreme values. We also find that the distribution of maxima obeys scaling and follows the Gumbel statistics. For a scale-free network model with heterogeneous nodes, we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maximum distribution. Moreover, we find that neither the Gumbel nor the Frechet statistics describe the data.

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