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Properties of Gabriel Graphs Relevant to Geographic Variation Research and the Clustering of Points in the Plane

1980/07/01 by David W. Matula, Robert R. Sokal · 3 citations
Environmental Science · Computer Science · Social Sciences · #Land Use and Ecosystem Services #Data Management and Algorithms #Geographic Information Systems Studies #State (computer science) #Sociology #Evolutionary ecology #Anthropology #Environmental ethics #Library science #Ecology #Philosophy #Biology #Computer science #Algorithm

paper · pdf · doi:10.1111/j.1538-4632.1980.tb00031.x

openalex publication_date 1980/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/24

Abstract

In geographic variation analysis in biology, one or more variables are commonly mapped onto a set of points in the plane, such points representing sampling station locahties or areal unit centroids.The variables may be interval (morphometric variables, population densities, gene frequencies), ordinal (ranks), or nominal (genotypes, species).Similar procedures are encountered in the application of the methods of statistical geography to other disciplines.Many of the techniques for analyzing such variables require the construction of a geographicconnectivity network or graph among the sampling station localities.In such geographic-connectivity graphs, one connects by lines those pairs of points thought in some geographic sense to represent adjacent localities.Thus the pattern of geographic variation of a variable is evaluated with regard to the interconnectedness of the sampling station localities for which the variable has been measured.These geographic-connectivity graphs play an important role in numerous applications, three of which might be singled out here.1.An approach to the regionalization problem defines regions as statistically homogeneous and geographically connected areas [ 6 ] .In such problems, the geographic connectedness is determined from the geographicconnectivity graph among the localities.Some other approaches to the regionalization problem (e. g., [5, 15, 20, 331) employ geographic-connectivity graphs as well.2. In many tests for randomness of geographic variation patterns [18, 22, 27 1, a connection matrix is essential to formulating a null hypothesis of random variation patterns.3. Application of the technique of spatial autocorrelation [4, 12, 13,26,31, 321 usually requires formulation of a geographic-connectivity graph for localities.

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