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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/772

Title: Development of hierarchy theory for digraphs using concentration theory based on a new type of Lorenz curve
Authors: EGGHE, Leo
Issue Date: 2002
Publisher: Elsevier
Citation: Mathematical and Computer Modelling, 36(4-5). p. 587-602
Abstract: In digraphs one has a hierarchy based on the unidirectional order between the vertices of the graph. We present a method of measuring degrees of hierarchy as expressed by the inequality that exists between the vertices' hierarchical numbers. In order to do so, we need to extend the classical Lorenz theory of concentration (curves and measures) for a set of numbers x1,…, xN to the case that ∑Ni=1 i = 0. This is then applied to the set of hierarchical numbers of the vertices of the graph. A graph has a more concentrated hierarchy than another one if the Lorenz curve of the first one is above the Lorenz curve of the second one, hereby expressing that the inequality in domination in the first case is larger than in the second case, and that the inequality in subordination in the first case is larger than in the second case. We also determine maximal and minimal Lorenz curves in this setting and characterize the graphs that yield these curves. Based on this theory, we also determine good measures of hierarchical concentration in graphs. Applications can be given in the study of organigrams in companies and administrations and in citation analysis
URI: http://hdl.handle.net/1942/772
DOI: 10.1016/S0895-7177(02)00184-X
ISI #: 000178418500014
ISSN: 0895-7177
Category: A1
Type: Journal Contribution
Validation: ecoom, 2003
Appears in Collections: Research publications

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