A local hierarchy theory for acyclic digraphs
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. (C) 2004 Elsevier Ltd. All rights reserved.
local hierarchy theory acyclic digraphs generalized lorenz curve organizational charts citation analysis global hierarchy theory