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


