How does degree heterogeneity affect an order-disorder transition?

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Abstract

We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the majority rule, applied to dichotomous networks. The latter are composed of two kinds of nodes, each kind i being characterized by a degree k. Dichotomous networks are therefore a simple instance of heterogeneous networks, especially adapted in order to reveal the effect of degree heterogeneity. Our main result are that degree heterogeneity affects the location of the order-disorder transition and that the system exhibits non-equipartition of the average opinion between the two kinds of nodes. This effect is observed in the ordered phase and in the disordered phase.
Original languageEnglish
JournalEPL
Volume78
Issue number6
DOIs
Publication statusPublished - 1 Jun 2007

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title = "How does degree heterogeneity affect an order-disorder transition?",
abstract = "We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the majority rule, applied to dichotomous networks. The latter are composed of two kinds of nodes, each kind i being characterized by a degree k. Dichotomous networks are therefore a simple instance of heterogeneous networks, especially adapted in order to reveal the effect of degree heterogeneity. Our main result are that degree heterogeneity affects the location of the order-disorder transition and that the system exhibits non-equipartition of the average opinion between the two kinds of nodes. This effect is observed in the ordered phase and in the disordered phase.",
author = "R. Lambiotte",
note = "Copyright 2011 Elsevier B.V., All rights reserved.",
year = "2007",
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doi = "10.1209/0295-5075/78/68002",
language = "English",
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How does degree heterogeneity affect an order-disorder transition? / Lambiotte, R.

In: EPL, Vol. 78, No. 6, 01.06.2007.

Research output: Contribution to journalArticle

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AU - Lambiotte, R.

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N2 - We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the majority rule, applied to dichotomous networks. The latter are composed of two kinds of nodes, each kind i being characterized by a degree k. Dichotomous networks are therefore a simple instance of heterogeneous networks, especially adapted in order to reveal the effect of degree heterogeneity. Our main result are that degree heterogeneity affects the location of the order-disorder transition and that the system exhibits non-equipartition of the average opinion between the two kinds of nodes. This effect is observed in the ordered phase and in the disordered phase.

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