TY - JOUR
T1 - Extremum Statistics in Scale-Free Network Models
AU - Moreira, André Auto
AU - Andrade, José S.
AU - Nunes Amaral, Luís A.
N1 - Funding Information:
We thank S. Mossa and H. E. Stanley for stimulating discussions and helpful suggestions. A. A. M. and J. S. A. thank the Brazilian Agencies CNPq and FUNCAP for support. L. A. N. A. thanks NIH/NCRR (P41 RR13622) and NSF for support.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.89.268703
DO - 10.1103/PhysRevLett.89.268703
M3 - Article
C2 - 12484864
AN - SCOPUS:0037165010
SN - 0031-9007
VL - 89
JO - Physical review letters
JF - Physical review letters
IS - 26
ER -