Weighted Evolving Networks

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...

For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be better described using weighted links as binary connections do not portray the complete information of the system. All these weighted networks evolve in a different environment by following different underlying mechanics. Researchers have wo...

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...

Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of real-world network systems. We propose a simple model of such co-evolving network dynamics, in which the diffusion of a resource over a weighted network and the resource-driven evolution of the link weights occur simultaneously. We demonstrate that,...

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...

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of non-homogeneous birth-and-death processes, and, with which, we capture the process by which the network connectivity evolves. We develop an effective algorithm to compute the network degree distribution accurately. Comparing analytical and numeric...

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...

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting networks have scale-free distributions of the edge weight, of the vertex degree, and of the vertex strength. We discuss situations where this mechanism operates. Apart of stochastic models of weighted networks, we introduce a wide class of determi...

We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via the simplest weight-driven rule: A newly-added node is connected to an already existing node with the probability which is proportional to the weight of that node. We show that the node weight distribution n(w) has a universal, that is inde...