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Summary: Physica A 346 (2005) 2026
Complex networks on hyperbolic surfaces
T. AsteÃ, T. Di Matteo, S.T. Hyde
Applied Mathematics, Research School of Physical Sciences, Australian National University,
0200 Canberra, Australia
Available online 17 September 2004
Abstract
We explore a novel method to generate and characterize complex networks by means of
their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the
exploration of the ensemble of networks which share common embeddings and consequently
share similar hierarchical properties. This method provides a new perspective to classify
network-complexity both on local and global scale. We demonstrate by means of several
examples that there is a strong relation between the network properties and the embedding
surface.
r 2004 Elsevier B.V. All rights reserved.
PACS: 89.75.Hc; 89.75.Àk; 89.65.Gh
Keywords: Networks; Complex systems; Hyperbolic graphs; Econophysics
1. Introduction
In recent years, it has become increasingly evident that a convenient way to study
complex systems constituted of many interacting elements is by associating to each
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