pcds.ugraph-package {pcds.ugraph}

pcds.ugraph: A package for the Underlying and Reflexivity Graphs of the Proximity Catch Digraphs and Their Applications

Description

pcds.ugraph is a package for construction and visualization of the underlying graphs based on proximity catch digraphs and for computation of edge density of these graphs for testing spatial patterns.

Details

The PCD families considered are Arc-Slice PCDs, Proportional-Edge PCDs and Central Similarity PCDs (Ceyhan (2005); Ceyhan et al. (2006); Ceyhan et al. (2007)).

The graph invariant used in testing spatial point data are the edge density of the underlying and reflexivity graphs of the PCDs (see Ceyhan (2016)).

The package also contains visualization tools for these graphs for 1D-3D vertices. The AS-PCD and CS-PCD related tools are provided for 1D and 2D data; PE-PCD related tools are provided for 1D-3D data.

The pcds.ugraph functions

The pcds.ugraph functions can be grouped as AS-PCD Functions, PE-PCD Functions, and CS-PCD Functions.

Arc-Slice PCD Functions

Contains the functions used in AS-PCD construction and computation of edge density of the corresponding underlying and reflexivity graph.

Proportional-Edge PCD Functions

Contains the functions used in PE-PCD construction and computation of edge density of the corresponding underlying and reflexivity graph.

Central-Similarity PCD Functions

Contains the functions used in CS-PCD construction and computation of edge density of the corresponding underlying and reflexivity graph.

Author(s)

Maintainer: Elvan Ceyhan [e-mail]

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2016). “Edge Density of New Graph Types Based on a Random Digraph Family.” Statistical Methodology, 33, 31-54.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

Ceyhan E, Priebe CE, Wierman JC (2006). “Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.” Computational Statistics & Data Analysis, 50(8), 1925-1964.