Hierarchical decompositions are a useful tool for drawing large graphs. Such decompositions can be represented by means of a data structure called hierarchy tree. In this paper we introduce the notion of P-validity of hierarchy trees with respect to a given property P: this notion reflects the similarity between the topological structure of the original graph and of any high-level representation of it obtained from the hierarchy tree. We study the P-validity when the clustered graph is a tree and property P is the acyclicity, presenting a structure theorem for the P-validity of hierarchy trees under these hypotheses.
CITATION STYLE
Finocchi, I., & Petreschi, R. (2001). On the validity of hierarchical decompositions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2108, pp. 368–374). Springer Verlag. https://doi.org/10.1007/3-540-44679-6_40
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