Mutual attraction model for both assortative and disassortative weighted networks

Abstract

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...

Emergence of scaling and assortative mixing through altruism

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A General BBV Model with High Clustering Scale-Free Networks

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“…Recently, several weighted network models were proposed [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Classes of weighted network with fixed topological structures are proposed [10][11][12].…”

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