Weighted evolving networks: coupling topology and weights dynamics

The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with some unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node deg...

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...

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...

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...

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...

We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the network is determined nonlocally, this approach can explain the generic nonlinear scaling between the strength and the degree of a node. We demonstrate by a simple model that the strength-driven evolution scheme recently introduced can be g...

Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the node connectivities and of the link weights. A weighted fitness network is introduced in which both nodes and links are assigned intrinsic fitness. This model can show a local dependence o...

We propose a model for the World Wide Web graph that couples the topological growth with the traffic's dynamical evolution. The model is based on a simple traffic-driven dynamics and generates weighted directed graphs exhibiting the statistical properties observed in the Web. In particular, the model yields a non-trivial time evolution of vertices and heavy-tail distributions for the topological and traffic properties. The generated graphs exhibit a complex architecture with ...

We discuss a newly proposed model by Barrat et al. (Phys. Rev. Lett. 92, 228701, 2004) for weighted evolving networks and suggest yet another model which can be viewed in the framework of worldwide airport network as "busy airports get busier".

Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered. Compared with the BA model and other evolving models with preferential attachment, there are two significant generalizations. First, besides the new vertex added in at every time step, old vertices can also attempt to build up new links, or to rec...