RandomGraph[SpatialGraphDistribution[n, r]] generates a random geometric graph over $[0,1]^2$ where vertices are connected if they are within a distance $r$ of one-another.
How would I explicitly specify a list of points for generating a random geometric graph using this function? Specifically, I need to enforce a minimum threshold distance between points.
Clarification: My point list is going to come from a Random Sequential Adsorption (RSA) simulation of circles on a plane. So I mean that no two points should be closer than some minimum threshold distance set by the radius of the circles being deposited, not that two points shouldn't share an edge if they are closer than the threshold distance.