Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very distant". This is in contrast to the more-studied cases of bond percolation and site percolation, the standard models for which allow flow only between adjacent edges and vertices, respectively. To make this intuition more precise, some authors describe long-range percolation to be a model in which any two elements x and y within some metric space (M, d) are connected by an edge e_(x y) = {x, y} with some probability p where p is inversely proportional to the distance d(x, y) between them .

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