The Evolution of Complex Networks: A New Framework

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting ...

We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices' properties and scale-free behavior for the weight, strength and degree distributions.

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 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 ...

We propose a unified modelling framework that theoretically justifies the main empirical regularities characterizing the international trade network. Each country is associated to a Polya urn whose composition controls the propensity of the country to trade with other countries. The urn composition is updated through the walk of the Reinforced Urn Process of Muliere et al. (2000). The model implies a local preferential attachment scheme and a power law right tail behaviour of...

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...

Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years. Another universal feature is observed in the power-law growth of the trade strength with gross dom...

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 biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total we...

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...