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Dynamics on modular networks with heterogeneous correlations
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10.1063/1.4869983
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.
© 2014 AIP Publishing LLC
Received 13 July 2012
Accepted 18 March 2014
Published online 16 April 2014
Lead Paragraph:
Many networks are constructed from multiple interconnected modules or contain multiple types of nodes or edges. The investigation of such networks has become increasingly prominent due to their importance for the consideration of interconnected real-world systems such as transportation networks with multiple modes of travel or the spread of social influence via multiple media. In this paper, we develop a model of networks that consist of multiple interconnected modules. This model generalizes several existing random-graph ensembles. We also present an analytical method to investigate a broad class of binary-state dynamics on such networks and use both synthetic and real-world data to illustrate situations that are well-captured by our theory but not by previous theories.
Acknowledgments:
S.M. acknowledges the INSPIRE fellowship funded by the Irish Research Council (co-funded by Marie Curie Actions under FP7). J.P.G. and S.M. acknowledge funding provided by Science Foundation Ireland under programmes 11/PI/1026. M.A.P. acknowledges a research award (#220020177) from the James S. McDonnell Foundation. M.A.P. and J.P.G. were supported by the European Commission FET-Proactive project PLEXMATH (Grant No. 317614). P.J.M. was funded by Award Number R21GM099493 from the National Institute of General Medical Sciences; the content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of General Medical Sciences or the National Institutes of Health. We thank Ali Faqeeh for useful discussions. We thank Adam D'Angelo and Facebook for providing the Facebook data. We also thank Cx-Nets collaboratory for making publicly available the protein interaction data set that we used in this study. This work was conceived in part during the 2010–2011 program year on Complex Networks at the Statistical and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle Park, NC, USA.
Article outline:
I. INTRODUCTION
II. DEFINITION AND CONSTRUCTION OF Pi,i'k,k′ NETWORKS
III. ANALYTICAL CALCULATION OF DYNAMICS ON Pi,i'k,k′ NETWORKS
IV. APPLICATION TO Pk,k′ AND Ei,i' NETWORKS
V. EXAMPLES OF DYNAMICS ON MODULAR SYNTHETIC Ei,i' NETWORKS
A. Bond percolation
B. Site percolation
C. Watts threshold model
VI. ADVANCED EXAMPLES
A. Synthetic Pi,i'k,k′ networks
B. LFR benchmark networks
C. Conjoined real-world networks
VII. CONCLUSIONS
/content/aip/journal/chaos/24/2/10.1063/1.4869983
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2014-04-16
2014-12-17
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