Volume 57, Number 3, February 2002
|Page(s)||334 - 340|
|Published online||01 September 2002|
Multifractal properties of growing networks
Departamento de Física and Centro de Física do Porto, Faculdade
de Ciências Universidade do Porto -
Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 A.F. Ioffe Physico-Technical Institute - 194021 St. Petersburg, Russia
Accepted: 9 September 2001
We introduce a new family of models for growing networks. In these networks new edges are preferentially attached to vertices with a higher number of connections, and new vertices are created by already existing ones, partially inheriting (partially copying) connections of their parents. We show that the combination of these two features produces multifractal degree distributions. Here degree is the number of connections of a vertex. An exact multifractal distribution is found for a nontrivial model of this class. The distribution tends to a power law form with in the infinite network limit. For finite networks, because of multifractality, any attempt to interpret the distribution as scale free will result in an ambiguous value of the exponent .
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 87.18.Sn – Neural networks
© EDP Sciences, 2002
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