Weighted Network Models Based on Local and Global Rules

Clustering coefficient is an important topological feature of complex networks. It is, however, an open question to give out its analytic expression on weighted networks yet. Here we applied an extended mean-field approach to investigate clustering coefficients in the typical weighted networks proposed by Barrat, Barth\'elemy and Vespignani (BBV networks). We provide analytical solutions of this model and find that the local clustering in BBV networks depends on the node degr...

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,...

With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has with the other nodes. For this purpose a network is modeled as a graph where nodes represent network members and edges represent a relationship among them. Several models for evolution of social networks has been proposed till date, most wi...

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...

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment...

In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary model results in weighted scale free networks. Indeed we find that in the one mode picture we have weighted networks with scale free distributions for interesting quantities like the weights, the degrees and the weighted degrees of the nodes a...

A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system constituents. However, it ignores the gradations of interactions commonly quantified by the link weight, w. Here, we identify an integrative weight organization for brain, gene, social, and language networks, in which strong links preferentially occu...

We extend the previously observed scaling equation connecting the internode distances and nodes' degrees onto the case of weighted networks. We show that the scaling takes a similar form in the empirical data obtained from networks characterized by different relations between node's strength and its degree. In the case of explicit equation for s(k) (e.g. linear or scale-free), the new coefficients of scaling equation can be easily obtained. We support our analysis with numeri...

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by degree, which are also the properties captured by different random graph models proposed in the literature. However, many (non-social) real-world networks are in fact disassortative by degree. Thus, we here propose a simple evolving model that ge...

Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization and studies of the density of hierarchical degrees in random and scale free networks. The obtained results allowed the identification of a hierarchy-dependent power law for the degrees of nodes in random complex networks, with Poisson density...