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1 Prace Naukowe Politechniki Warszawskiej. Elektronika

1 2006

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Scale free distribution of nodes in Euclidean graphs

Dominik A., Walczak Z., Wojciechowski J., Wojciechowski J.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2006

z. 156

107-115

In the paper we propose a new model of spatial distribution of nodes in graphs which can be represented in the Euclidean space. Such graphs appear in many areas of computer science, for instance wireless networks design, Traveling Salesman and Vehicle Routing Problems. We show analogies between scale-free and Euclidean graphs. Although the distribution of node's degrees in Euclidean graphs is not scale-free, the spatial distribution of node's follows the power law. We analyze distribution of population density in different continents, propose a model to generate such distributions and provide numerical experiments concerning its quality. Finally, the impact of our model on different NP-complete problems in Euclidean graphs is analyzed.