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Title: Dynamics on modular networks with heterogeneous correlations

Abstract

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.

Authors:
 [1];  [2];  [2];  [3];  [2];  [4];  [5];  [1]
  1. MACSI, Department of Mathematics and Statistics, University of Limerick (Ireland)
  2. (United Kingdom)
  3. Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
  4. Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250 (United States)
  5. (United States)
Publication Date:
OSTI Identifier:
22250790
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; CORRELATIONS; DIAGRAMS; GRAPH THEORY; RANDOMNESS

Citation Formats

Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 27599-3216, and Gleeson, James P.. Dynamics on modular networks with heterogeneous correlations. United States: N. p., 2014. Web. doi:10.1063/1.4869983.
Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 27599-3216, & Gleeson, James P.. Dynamics on modular networks with heterogeneous correlations. United States. doi:10.1063/1.4869983.
Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 27599-3216, and Gleeson, James P.. Sun . "Dynamics on modular networks with heterogeneous correlations". United States. doi:10.1063/1.4869983.
@article{osti_22250790,
title = {Dynamics on modular networks with heterogeneous correlations},
author = {Melnik, Sergey and Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP and Porter, Mason A. and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP and Mucha, Peter J. and Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 27599-3216 and Gleeson, James P.},
abstractNote = {We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.},
doi = {10.1063/1.4869983},
journal = {Chaos (Woodbury, N. Y.)},
number = 2,
volume = 24,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}
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