Size of the giant component in a random geometric graph
A random geometric graph \(G\) is defined with \(n\) nodes that are independently selected according to a common probability distribution with density \(f\) in the unit square. Two nodes are joined by an edge if their distance is less than a specified positive value \(r=r(n)\). The density \(f\) is assumed to have its infimum and its supremum strictly between 0 and infinity. By dividing the unit square into subsquares, so that nodes in adjacent subsquares can be joined by an edge, a technique is developed to investigate the structure of the giant component for a certain range of values of \(r\). Size and diameter are estimated as \(n\) tends to infinity and \(r\) is proportional to the square root of \(1/n\) or of \((\log n)/n\). Both uniform and non-uniform \(f\) are considered.
scientific article; zbMATH DE number 6229201