Abstract
It is shown that a graph called the minimal spanning tree (MST) is capable of detecting several kinds of cluster structure in arbitrary points set. From a MST it is possible to deduce the average edge length m and the standard deviation σ, which are characteristics for the corresponding distribution. The use of a diagram involving both m and σ makes it possible to determine the degree of order by taking a simple reading in the (m, σ) plane. It is also possible, through angular diagrams retrieved from the MST, to bring out directional properties. The method is applied to the study of the growth of granular thin films.
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References
Zahn, CT.: IEEE Trans. Comput. C 20, 68 (1971).
Dussert, C, Rasigni, G., Rasigni, M., Palmari, J., Llebaria, A.: Phys. Rev. B 34, 3528 (1986).
Rasigni, M., Rasigni, G., Palmari, J.P., Llebaria, A.: J. Opt. Soc. Am. 71, 1124 (1981).
Rohlf, F.J.: Computer. J. 16, 93 (1973).
Hoffman, R., Jain, A.K.: Pattern Recognit. Lett. 1, 175 (1983).
Stevens, P.J.: Les formes dans la nature. Paris: Editions du Seuil 1978.
Knuth, D.E.: The art of computer programming. New York: Addison Wesley 1969.
Venables, J.A., Spiller, G.D.T., Nanücken, M.: Rep. Prog. Phys. 47, 399 (1984).
Diggle, P.J.: Statistical analysis of spatial points patterns. London: Academic Press 1983.
Bassett, G.A., Menker, J.W., Pashley, D.W.: In: Structure and properties of thin films. Neugebauer, C.A., New-Kirk, J.B., Vermilyea, D.A., (eds.), p. 11. New York: Wiley 1959.
Dussert, C, Rasigni, G, Llebaria, A.: J. Theor. Biol. 135, 295 (1988).
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© 1989 Springer-Verlag
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Dussert, C., Rasigni, G., Rasigni, M., Palmari, J., Llebaria, A. (1989). Minimal spanning tree analysis of regular, random and cluster structures. In: Chapon, C., Gillet, M.F., Henry, C.R. (eds) Small Particles and Inorganic Clusters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74913-1_10
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DOI: https://doi.org/10.1007/978-3-642-74913-1_10
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