Egghe L. "Development of hierarchy theory for digraphs using concentration theory based on a new type of Lorenz curve" MATHEMATICAL AND COMPUTER MODELLING 36 (4-5): 587-602 SEP 2002
Eugene Garfield
garfield at CODEX.CIS.UPENN.EDU
Mon Dec 2 15:30:26 EST 2002
Leo Egghe : leo.egghe at luc.ac.be
Title Development of hierarchy theory for digraphs using
concentration theory based on a new type of Lorenz curve
Author Egghe L
Journal MATHEMATICAL AND COMPUTER MODELLING 36 (4-5): 587-602 SEP 2002
Document type: Article Language: English
Cited References: 17 Times Cited: 0
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 x(1),..., x(N) to the case that
Sigma(i=1)(N) x(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. (C) 2002 Elsevier Science Ltd. All
rights reserved.
Author Keywords:
digraph, hierarchy, Lorenz, concentration theory
KeyWords Plus:
INEQUALITY, METRICS
Addresses:
Egghe L, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium
Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium
Univ Instelling Antwerp, B-2610 Wilrijk, Belgium
Publisher:
PERGAMON-ELSEVIER SCIENCE LTD, OXFORD
IDS Number:
600YC
ISSN:
0895-7177
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DEBRA P SCIENTOMETRICS 47 227 2000
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GINI C GIORNALE DEGLI EC 11 37 1909
HARDY GH INEQUALITIES 1952
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LORENZ MO J AM STAT ASSOC 9 209 1905
MARSHALL AW MATH SCI ENG 143 1979
MUIRHEAD RF P EDINBURGH MATH SOC 21 144 1903
REID RC ENUMERATION GRAPH CO 1997
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SHANNON C BELL SYSTEM J 28 379 1948
THEIL H EC INFORMATION THEOR 1967
WILSON BJ INTRO GRAPH THEORY 1972
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_______________________________________________________________________
Eugene Garfield, PhD. email: garfield at codex.cis.upenn.edu
home page: www.eugenegarfield.org
Tel: 215-243-2205 Fax 215-387-1266
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