Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule

Abstract

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its neighbouring local nodes for connection and is not controlled by the preferential attachment as in the Barabási-Albert (BA) model. This observation has been mimicked in our model where the nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link. In spite of this crucial difference it is observed that the leading behaviour of our network is like the BA model. Defining link weight as an algebraic power of its Euclidean length, the weight distribution and the non-linear dependence of the nodal strength on the degree are analytically calculated. It is claimed that a power law decay of the link weights with time ensures such a non-linear behavior. Switching off the Euclidean space from the same model yields a much simpler definition of the Barabási-Albert model where numerical effort grows linearly with $N$.

6 pages, 6 figures

References in corpus (12)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• The architecture of complex weighted networks
• Evolution of networks
• Dynamical and correlation properties of the Internet
• Organization of Growing Random Networks
• Modeling the Internet's Large-Scale Topology
• General Dynamics of Topology and Traffic on Weighted Technological Networks
• Modulated Scale-free Network in the Euclidean Space
• Emergence of weight-topology correlations in complex scale-free networks
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• Effects of accelerating growth on the evolution of weighted complex networks
• Geometric origin of scaling in large traffic networks
• The International Trade Network
• An optimal network for passenger traffic
• Limit theorems for random spatial drainage networks
• Branching Process in a Stochastic Extremal Model
• Heterogeneous network with distance dependent connectivity
• Analytic Solution to Clustering Coefficients on Weighted Networks
• A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution