Minimal models of weighted scale-free networks

Abstract

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting networks have scale-free distributions of the edge weight, of the vertex degree, and of the vertex strength. We discuss situations where this mechanism operates. Apart of stochastic models of weighted networks, we introduce a wide class of deterministic, scale-free, weighted graphs with the small-world effect. We show also how one can easily construct an equilibrium weighted network by using a generalization of the configuration model.

11 pages, 9 figures

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Cited by in corpus (6)

• Weighted Fractal Networks
• The Role of Weight on Community Structure of Networks
• Degree-dependent intervertex separation in complex networks
• Construction of bipartite and unipartite weighted networks from collections of journal papers
• Universality of competitive networks for weighted networks
• A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution