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Extremum Statistics in Scale-Free Network Models Andre Auto Moreira,1,2,* Jose S. Andrade, Jr.,2,

Summary: Extremum Statistics in Scale-Free Network Models
Andre´ Auto Moreira,1,2,* Jose´ S. Andrade, Jr.,2,
and Lui´s A. Nunes Amaral1,3,
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
Departamento de Fi´sica, Universidade Federal do Ceara´, 60451-970 Fortaleza, Ceara´, Brazil
Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60208
(Received 29 April 2002; published 12 December 2002)
We investigate the statistics of the most connected node 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 and that the distribution of maxima 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 maxima distribution.
DOI: 10.1103/PhysRevLett.89.268703 PACS numbers: 89.75.Hc, 05.10.­a
The statistics of extrema is a classical subject of great
interest in mathematics and physics [1]. In physics, ex-
treme events have been studied in a number of fields,


Source: Amaral, Luis A.N. - Department of Chemical and Biological Engineering, Northwestern University


Collections: Physics; Biology and Medicine