### Abstract

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping Y' (Y-μ)/(1-μ) describes how a shift of the standard exponent Y of the degree distribution can absorb the effect of degree-dependent pair interactions Jij (ki kj)μ, where ki stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

Original language | English |
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Article number | 036108 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 74 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2006 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*74*(3), [036108]. https://doi.org/10.1103/PhysRevE.74.036108

**Criticality on networks with topology-dependent interactions.** / Giuraniuc, C. V.; Hatchett, J. P.L.; Indekeu, J. O.; Leone, M.; Pérez Castillo, I.; Van Schaeybroeck, B.; Vanderzande, C.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 74, no. 3, 036108. https://doi.org/10.1103/PhysRevE.74.036108

}

TY - JOUR

T1 - Criticality on networks with topology-dependent interactions

AU - Giuraniuc, C. V.

AU - Hatchett, J. P.L.

AU - Indekeu, J. O.

AU - Leone, M.

AU - Pérez Castillo, I.

AU - Van Schaeybroeck, B.

AU - Vanderzande, C.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping Y' (Y-μ)/(1-μ) describes how a shift of the standard exponent Y of the degree distribution can absorb the effect of degree-dependent pair interactions Jij (ki kj)μ, where ki stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

AB - Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping Y' (Y-μ)/(1-μ) describes how a shift of the standard exponent Y of the degree distribution can absorb the effect of degree-dependent pair interactions Jij (ki kj)μ, where ki stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

UR - http://www.scopus.com/inward/record.url?scp=33748788506&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.74.036108

DO - 10.1103/PhysRevE.74.036108

M3 - Article

VL - 74

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 3

M1 - 036108

ER -