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suppose nodes with radius R are distributed randomly in Area of size A, then how can we calculate the degree of each node by geometric random graph.

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If the nodes are Poisson distributed the degree of a node is Poisson with mean given by the expected number of nodes within range (depending on the density, range $R$ and how close to the boundary). If instead the nodes have a fixed number and are uniformly distributed, there are small corrections to this. For more details, try

Mathew Penrose Random geometric graphs. Oxford University Press, 2003.

Mark Walters Random geometric graphs, in Surveys in Combinatorics, 2011.

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