A local hierarchy theory for acyclic digraphs

Authors:
L Egghe;R Rousseau
Affiliations:
-;LUC, Universitaire Campus, B-3590 Diepenbeek, Belgium and UA, Universiteitsplein 1, B-2610 Wilrijk, Belgium
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2004

Citing 2
Cited 1

Structural analysis of hypertexts: identifying hierarchies and useful metrics

ACM Transactions on Information Systems (TOIS)
Development of hierarchy theory for digraphs using concentration theory based on a new type of Lorenz curve

Mathematical and Computer Modelling: An International Journal

Acyclic digraphs and local hierarchy theory

Mathematical and Computer Modelling: An International Journal

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Abstract

Local hierarchy theory focuses on direct links in acyclic digraphs. In- and out-degrees are used to determine the local hierarchical number for each vertex in the graph. Together, these local hierarchical numbers form a vector through which hierarchical properties are studied. The main tool, leading to a partial order of acyclic digraphs is a form of generalized Lorenz curve. Gini-like measures respecting this partial order can be derived. Local hierarchy theory is then the theory related to this particular partial order. Results have possible applications in administration and business organizational charts and in citation analysis. In the latter, a direct link represents a reference or a citation of a document. Finally, we study rooted trees as a concrete example of local hierarchy theory.