June 10, 2004
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 non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial 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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January 6, 2004
We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices' properties and scale-free behavior for the weight, strength and degree distributions.
July 14, 2006
Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by topological growth as well as by weight change. In addition, we introduce the weighted assortativity coefficient, which generalizes the assortativity coefficient of a topological network, to measure the tendency of having a high-weighted lin...
January 19, 2001
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total we...
May 17, 2005
We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for example, the power-law distributions and evolution of degree, weight and strength. We also study the nontrivial clustering coefficient C and tunable degree assortativity coefficient r, depending on specific parameters. Most results are supp...
May 17, 2005
We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for example, the power-law distributions and evolution of degree, weight and strength. We also study the nontrivial clustering coefficient C and tunable degree assortativity coefficient r, depending on specific parameters. Most results are supp...
January 10, 2005
For most technical networks, the interplay of dynamics, traffic and topology is assumed crucial to their evolution. In this paper, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general strength-coupling mechanism under which the traffic and topology mutually interact, the model gives power-law distributions of degree, weight and strength, as confirmed in many real networks. Particularly, depending on a parameter W that contro...
January 15, 2007
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to existing nodes but also by self-growing weight of existing links based on a simple weight-driven rule. This model is analytically tractable, so that the various statistical properties, such as the distribution of weight, can be derived. Fina...
April 13, 2007
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for the evolutions and distributions for strength, degree, and weight, which are relevant to accelerating growth. We also find that accelerating growth determines the clustering coefficient of the networks. Interestingly, the distributions for s...
September 7, 2007
We propose a synthetical weights' dynamic mechanism for weighted networks which takes into account the influences of strengths of nodes, weights of links and incoming new vertices. Strength/Weight preferential strategies are used in these weights' dynamic mechanisms, which depict the evolving strategies of many real-world networks. We give insight analysis to the synthetical weights' dynamic mechanism and study how individual weights' dynamic strategies interact and cooperate...
August 3, 2009
We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by assuming that link weights evolve according to a geometric Brownian motion. Our model is verified by means of simulations and real world trade data. We show that the model correctly predicts the intensity and growth distribution of links, the si...