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Classes of small-world networks L. A. N. Amaral*, A. Scala, M. Barthelemy

Summary: Classes of small-world networks
L. A. N. Amaral*, A. Scala, M. BartheŽleŽmy
, and H. E. Stanley
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215
Communicated by Herman Z. Cummins, City College of the City University of New York, New York, NY, July 13, 2000 (received for review April 20, 2000)
We study the statistical properties of a variety of diverse real-world
networks. We present evidence of the occurrence of three classes
of small-world networks: (a) scale-free networks, characterized by
a vertex connectivity distribution that decays as a power law; (b)
broad-scale networks, characterized by a connectivity distribution
that has a power law regime followed by a sharp cutoff; and (c)
single-scale networks, characterized by a connectivity distribution
with a fast decaying tail. Moreover, we note for the classes of
broad-scale and single-scale networks that there are constraints
limiting the addition of new links. Our results suggest that the
nature of such constraints may be the controlling factor for the
emergence of different classes of networks.
Disordered networks, such as small-world networks are the
focus of recent interest because of their potential as models
for the interaction networks of complex systems (1­7). Specifi-


Source: Amaral, Luis A.N. - Department of Chemical and Biological Engineering, Northwestern University
Stanley, H. Eugene - Department of Physics, Boston University


Collections: Biology and Medicine; Computer Technologies and Information Sciences; Materials Science; Physics