The K-Function Method on a Network and its Computational Implementation

This paper proposes two statistical methods, called the network K-function method and the network cross K-function method, for analyzing the distribution of points on a network. The former method is used for testing the hypothesis that points are uniformly and independently distributed over a network. The latter method is used for testing the hypothesis that points of one kind and points of another kind are independently distributed over a network. The paper first derives the equations of these functions. Second, these equations are implemented in computational procedures. Third, the computational orders of these procedures are obtained: the order of the K-function method is O(nQ log nQ) and that for the network cross K-function is O(nQ log nQ), where nQ is the number of nodes of a network.