This paper investigates the role of asymmetrical degree-dependent weighted couplings in synchronization of a network of Kuramoto oscillators, where the conditions of coupling criticality for the onset of phase synchronization in degree-weighted complex networks are arrived at. The numerical...

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...

In the present study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be...

Extending previous work on unweighted networks, we present here a systematic numerical investigation of standard evolutionary games on weighted networks. In the absence of any reliable model for generating weighted social networks, we attribute weights to links in a few ways supported by...

General conditions for the appearance of the power-law distribution of total weights concentrated in vertices of complex network systems are established. By use of the rate equation approach for networks evolving by connectivity-governed attachment of every new node to p⩾1 exiting nodes and by...

An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the nodes of the abstract network. Transitions between the...

In this paper, we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure. In the model, the nodes in the network are represented by the traffic...

Network systems evolving by preferential attachment of new vertices and by link loading are considered. The probability of node attaching is assumed to depend linearly on degrees of existing nodes to which new ones are connected. The rule of the network loading allows both deterministic and...

We introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links. The class of resulting algorithms for different parameter values includes the Barabási–Albert...

In this paper, we propose an evolutionary model for weighted networks by introducing an age-based mutual selection mechanism. Our model generates power-law distributions of degree, weight, and strength, which are confirmed by analytical predictions and are consistent with real observations. The...