Erratum: Apollonian Networks: Simultaneously Scale-Free, Small World, Euclidean, Space Filling, and with Matching Graphs [Phys. Rev. Lett.<b>94</b>, 018702 (2005)]

Andrade, José S.; Herrmann, Hans J.; Andrade, Roberto F. S.; Silva, Luciano R. da

doi:10.1103/physrevlett.102.079901

Cited by 113 publications

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“…In the last five years, the Apollonian network (AN) [1] has attracted a lot of attention from the community working on models on non-Euclidean lattices. In particular complex networks [2][3][4] found widespread use in the investigation of most diverse scientific topics, as they can be able to represent connections between individual degrees of freedom in many complex systems.…”

Section: Introductionmentioning

confidence: 99%

q-state Potts model on the Apollonian network

2010

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The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, q. Different scaling functions in temperature and q are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

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Section: Introductionmentioning

confidence: 99%

q-state Potts model on the Apollonian network

2010

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“…The scaling C(k) ∼ k −1 has been found for some network models [7,10,12,17,44], and has also observed in several real-life networks [7]. Using Eq.…”

Section: Clustering Coefficientmentioning

confidence: 59%

“…To understand the general principles in architectures of networks, many deterministic models are introduced into complex networks [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, These models are useful tools for investigating analytically not only topological features of networks in detail [1,2,3,4,5,6,7,8,9,10,11,12], but also dynamical problems on the networks [13,14,15,16]. Before presenting our own findings, it is worth reviewing some of this preceding work to understand its achievements and shortcomings.…”

Section: Introductionmentioning

confidence: 99%

“…[8] and [9], respectively. Recently, motivated by the problem of Apollonian space-filing packing, Apollonian networks [10] with a typical loop structure were introduced and intensively investigated [17,18,19,20,21]. These pioneering works are all invaluable tools for the topology of networks studies.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, previous deterministic models, are mainly unweighted [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], which ignore the heterogeneity of edges in real networks. What's more, the models [3,4] on PSW networks fail to provide the reason for adopting the recursive way to build up the networks.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic weighted scale-free small-world networks

Zhang

Zhou

et al. 2010

Physica A: Statistical Mechanics and its Applications

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We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks: weight and strength distribution; degree correlations; average clustering coefficient and degree-cluster correlations; as well as the diameter.

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Topological evolution in dense granular materials: A complex networks perspective

Walker

Tordesillas

2010

International Journal of Solids and Structures

124

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a b s t r a c tOne of the great challenges in the science of complex materials -materials capable of emergent behavior such as self-organized pattern formation -is deciphering their ''inherent" structural design principles as they deform in response to external loads. We have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to: (i) uncover such design principles and (ii) identify suitable metrics that quantify the evolution of structure during deformation. Herein, we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks. Attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level, i.e., a particle and its immediate neighbors, as well as the macroscopic level. We explore network motifs and other topological properties at these multiple length scales, in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation, spatially and with respect to strain. Key processes or rearrangement events that cause loss of connectivity within the material domain, e.g. microbanding and force chain buckling, are investigated. Network statistics of these processes, previously shown to be major sources of energy dissipation and nonaffine deformation, are then tied to corresponding trends observed in the evolving macroscopic network. It is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity.

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Erratum: Apollonian Networks: Simultaneously Scale-Free, Small World, Euclidean, Space Filling, and with Matching Graphs [Phys. Rev. Lett.94, 018702 (2005)]

Cited by 113 publications

References 0 publications

q-state Potts model on the Apollonian network

q-state Potts model on the Apollonian network

Deterministic weighted scale-free small-world networks

Topological evolution in dense granular materials: A complex networks perspective

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