Weighted Evolving Networks

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of...

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number ...

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...

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...

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two limiting cases and numerical simulations the phase diagram of the model is obtained. In the stationary limit, large network sizes, a phase transition from a network with finite average connectivity to a network with a power law distributio...

Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In this letter we propose a new mechanism for the construction of SF networks: Evolving networks as interaction networks of systems which are distinguished by their stability if perturbed out of equilibrium. Stability is measured by the largest r...

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we extend the concept of evolving models of complex networks to hypernetworks. In this work, we firstly propose a non-uniform hypernetwork model with attractiveness, and obtain the stationary average hyperdegree distribution of the non-uniform hype...

In the paper, we present an incremental approach in the construction of scale free networks with hidden variables. The work arises from the necessity to generate that type of networks with a given number of links instead of obtaining a random configurations for a given set of parameters as in the usual literature. I propose an analytical approach of network evolution models gathering information along time based on the construction of a stochastic process on the space of poss...

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical infrastructures and social systems, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and...

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 a...