authorGergely Palla, László Lovász and Tamás Vicsek
year2010
titleMultifractal network generator
journalPROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
volume107
number17
pages7640-7645
projectmultifractal_network_generation
doi10.1073/pnas.0912983107
project_groupcomplex_networks
selectedtrue
unique-idISI:000277088700011
monthAPR 27
issn0027-8424
abstract
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed statistical properties, e. g., with degree or clustering coefficient distributions of various, very different forms. In turn, these graphs can be used to test hypotheses or as models of actual data. The method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks. Such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies. The main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously. A very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured. We present analytic expressions derived from the parameters of the-to be iterated-initial generating measure for such major characteristics of graphs as their degree, clustering coefficient, and assortativity coefficient distributions. The optimal parameters of the generating measure are determined from a simple simulated annealing process. Thus, the present work provides a tool for researchers from a variety of fields (such as biology, computer science, biology, or complex systems) enabling them to create a versatile model of their network data.

BibTex record:

@article{ ISI:000277088700011,
author = {Gergely Palla and László Lovász and Tamás Vicsek},
year = {2010},
title = {Multifractal network generator},
journal = {PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA},
volume = {107},
number = {17},
pages = {7640-7645},
project = {multifractal_network_generation},
doi = {10.1073/pnas.0912983107},
project_group = {complex_networks},
selected = {true},
unique-id = {ISI:000277088700011},
month = {APR 27},
issn = {0027-8424},
abstract = {We introduce a new approach to constructing networks with realistic features. Our method, in spite
of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of
network types with prescribed statistical properties, e. g., with degree or clustering coefficient
distributions of various, very different forms. In turn, these graphs can be used to test hypotheses
or as models of actual data. The method is based on a mapping between suitably chosen singular
measures defined on the unit square and sparse infinite networks. Such a mapping has the great
potential of allowing for graph theoretical results for a variety of network topologies. The main
idea of our approach is to go to the infinite limit of the singular measure and the size of the
corresponding graph simultaneously. A very unique feature of this construction is that with the
increasing system size the generated graphs become topologically more structured. We present
analytic expressions derived from the parameters of the-to be iterated-initial generating measure
for such major characteristics of graphs as their degree, clustering coefficient, and assortativity
coefficient distributions. The optimal parameters of the generating measure are determined from a
simple simulated annealing process. Thus, the present work provides a tool for researchers from a
variety of fields (such as biology, computer science, biology, or complex systems) enabling them to
create a versatile model of their network data.},
}