Weighted scale-free networks with stochastic weight assignments

Zheng, Dafang; Trimper, Steffen; Zheng, Bo; Hui, P. M.

doi:10.1103/physreve.67.040102

Cited by 87 publications

(57 citation statements)

References 30 publications

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“…Vertices entering the system draw new edges with an attachment dynamics driven by the weight properties of existing edges and vertices. In addition, in contrast with previous models [18,19] for which weights are statically assigned, we allow for the dynamical evolution of weights during the growth of the system. This dynamics is inspired by the evolution and reinforcements of interactions in natural and infrastructure networks.…”

Section: Introductionmentioning

confidence: 99%

Modeling the evolution of weighted networks

2004

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We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several realworld systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree.

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Section: Introductionmentioning

confidence: 99%

Modeling the evolution of weighted networks

2004

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“…In this letter, we will present a model for weighted evolving networks that considers the topological evolution under the general mechanism of mutual attraction between nodes. In contrast with previous models where weights are assigned statically [19,20] or rearranged locally [12,13], our model allow weights to be widely updated. It can mimic the reinforcement and creation of internal links as well as the evolution of many infrastructure networks.…”

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confidence: 99%

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confidence: 99%

Mutual attraction model for both assortative and disassortative weighted networks

Wang

et al. 2006

Phys. Rev. E

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In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial attractiveness A and the general mechanism of mutual attraction (controlled by parameter m), the model can naturally reproduce scale-free distributions of degree, weight and strength, as found in many real systems. Simulation results are in consistent with theoretical predictions. Interestingly, we also obtain nontrivial clustering coefficient C and tunable degree assortativity r, depending on m and A. Our weighted model appears as the first one that unifies the characterization of both assortative and disassortative weighted networks.PACS numbers: 02.50. Le, 05.65.+b, 87.23.Ge, 87.23.Kg The past few years have witnessed a great deal of interest from physics community to understand and characterize the underlying mechanisms that govern complex networks. Prototypical examples cover as diverse as the Internet [1], the World-Wide Web [2], the scientific collaboration networks (SCN) [3,4], and world-wide airport networks (WAN) [5,6]. As a landmark, Barabási and Albert (BA) proposed their seminal model that introduces the linear preferential linking to mimic the topological evolution of complex networks [7]. However, networks are far from boolean structure. The purely topological characterization will miss important attributes often encountered in real systems. For example, the amount of traffic characterizing the connections of communication systems or large transport infrastructure is fundamental for a full description of these networks [8]. This thus calls for the use of weighted network representation, which is often denoted by a weighted adjacency matrix with element w ij represents the weight on the edge connecting vertices i and j. In the case of undirected graphs, weights are symmetric w ij = w ji , as this letter will focus on. A natural generalization of connectivity in the case of weighted networks is the vertex strength described as s i = j∈Γ(i) w ij , where the sum runs over the set Γ(i) of neighbors of node i. This quantity is a natural measure of the importance or centrality of a vertex in the network. Most recently, the access to more complete empirical data and higher computation capability has allowed scientists to consider the variation of the connection weights of many real graphs. As confirmed by measurements, complex networks not only exhibit a scale-free degree distribution P (k) ∼ k −γ with 2≤ γ ≤3 [5, 6], but also the power-law weight distribution P (w) ∼ w −θ [9] and the strength distribution P (s) ∼ s −α [6]. Highly * Electronic address: hubo25@mail.ustc.edu.cn correlated with the degree, the strength usually displays scale-free property s ∼ k β with β ≥ 1 [6, 10, 11]. Motivated by those findings, Alain Barrat et al. presented a model (BBV for short) to study the growth of weighted networks [12]. Controlled by a single parameter δ, BBV model can produ...

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“…The diversity of scale-free characteristics, nontrivial clustering coefficient, assortativity coefficient and nonlinear strength-degree correlation that have been empirically observed can be well explained by our microscopic mechanisms. Moreover, in contrast with previous models where weights are assigned statically [17,18] or rearranged locally [10], we allow weights to be widely updated.…”

Section: Introductionmentioning

confidence: 99%

Mutual selection model for weighted networks

Wang

Zhou

et al. 2005

Phys. Rev. E

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For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of mutual selection, the model can produce powerlaw distributions of degree, weight and strength, as confirmed in many real networks. Moreover, we also obtained the nontrivial clustering coefficient C, degree assortativity coefficient r and degreestrength correlation, depending on a model parameter m. These results are supported by present empirical evidences. Studying the degree-dependent average clustering coefficient C(k) and the degree-dependent average nearest neighbors' degree knn(k) also provide us with a better description of the hierarchies and organizational architecture of weighted networks.

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Weighted scale-free networks with stochastic weight assignments

Cited by 87 publications

References 30 publications

Modeling the evolution of weighted networks

Modeling the evolution of weighted networks

Mutual attraction model for both assortative and disassortative weighted networks

Mutual selection model for weighted networks

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