The K‐Function Method on a Network and Its Computational Implementation

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Abstract
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. First, by extending the ordinary K‐function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K‐function method and the cross K‐function method on a finite irregular network with the shortest‐path distance. Second, the paper shows advantages of the network K‐function methods, such as that the network K‐function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K‐functions, and shows that the computational order of the K‐function method is O(n2Q log nQ) and that of the network cross K‐function is O(nQ log U3Q), where nQ is the number of nodes of a network.