In this paper we propose a model of the spatially distributed network based on the spatially correlated preferentialattachments. Nodes in the spatially distributed networks of the real word, such as various urban or biologicalnetworks, aren't establishing randomly: the probability of emergence of new nodes is higher in the area of alreadyexisting ones. In this work we unite two principles of the real network modeling: the correlated percolationmodel and preferential attachment. To regulate spatial limitations of the network, we use density gradient,which determines the decrease of the probability of the connection emergence between two nodes with increaseof the distance between them. We also consider the consistency of our results in the context of the real-worldsystem modeling.
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