Systematic series expansions for processes on networks

We use series expansions to study dynamics of equilibrium and nonequilibrium systems on networks. This analytical method enables us to include detailed nonuniversal effects of the network structure. We show that even low order calculations produce results which compare accurately to numerical simula...

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Bibliographic Details
Published in:Physical review letters 2006-04, Vol.96 (14), p.148701-148701, Article 148701
Main Author: Hastings, M B
Format: Article
Language:English
Subjects:
Computational Biology
Computer Simulation
Monte Carlo Method
Neural Networks (Computer)
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Summary:We use series expansions to study dynamics of equilibrium and nonequilibrium systems on networks. This analytical method enables us to include detailed nonuniversal effects of the network structure. We show that even low order calculations produce results which compare accurately to numerical simulation, while the results can be systematically improved. We show that certain commonly accepted analytical results for the critical point on networks with a broad degree distribution need to be modified in certain cases due to disassortativity; the present method is able to take into account the assortativity at sufficiently high order, while previous results correspond to leading and second order approximations in this method. Finally, we apply this method to real-world data.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.96.148701