Weighted evolving networks: coupling topology and weights dynamics

This paper presents an evolution model of weighted networks in which the structural growth and weight dynamics are driven by human behavior, i.e. passenger route choice behavior. Transportation networks grow due to people's increasing travel demand and the pattern of growth is determined by their route choice behavior. In airline networks passengers often transfer from a third airport instead of flying directly to the destination, which contributes to the hubs formation and f...

Inspired by studies on airline networks we propose a general model for weighted networks in which topological growth and weight dynamics are both determined by cost adversarial mechanism. Since transportation networks are designed and operated with objectives to reduce cost, the theory of cost in micro-economics plays a critical role in the evolution. We assume vertices and edges are given cost functions according to economics of scale and diseconomics of scale (congestion ef...

We propose and study a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows the weights of links are driven either by the connectivity with probability $p$ or by the fitness with probability $1-p$. Results of numerical simulations show that the total weight associated with a selected node exhibits a power law distribution with an exponent...

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial complexes are weighted. Here we propose a non-equilibrium model for weighted growing simplicial complexes. The proposed dynamics is able to generate weighted simplicial complexes with a rich interplay between weights and topology emerging not jus...

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...

In this paper, we propose a self-learning mutual selection model to characterize weighted evolving networks. By introducing the self-learning probability $p$ and the general mutual selection mechanism, which is controlled by the parameter $m$, the model can reproduce scale-free distributions of degree, weight and strength, as found in many real systems. The simulation results are consistent with the theoretical predictions approximately. Interestingly, we obtain the nontrivia...

We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical evidence that in many real networks there is a subset of "dominant edges" that control a major share of the total weight of the network. Furthermore, we introduce a new statistical procedure to study the evolution of networks over time, asses...

The population structure often impacts evolutionary dynamics. In constant-selection evolutionary dynamics between two types, amplifiers of selection are networks that promote the fitter mutant to take over the entire population, and suppressors of selection do the opposite. It has been shown that most undirected and unweighted networks are amplifiers of selection under a common updating rule and initial condition. Here, we extensively investigate how edge weights influence se...

Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local interactions non-trivial global phenomena can emerge as small-world properties or scale-free degree distributions. A simple model for the evolution of acquaintance networks highlights the essential dynamical ingredients necessary to obtain such...

We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a network may be viewed as an optimization of efficiency by minimizing redundancy. It is also a mechanism to shorten the distance and thus decrease signaling times between vertices in a complex network. Thus the merging process will in particul...