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Nested hierarchies in planar graphs

Song, Won-Min; Di Matteo, Tiziana; Aste, Tomaso


We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named 'bubbles', that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tree structure where neighboring bubbles are joined together by a 3-clique. Bubbles naturally provide the subdivision of G into communities and the tree structure defines the...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Discrete Applied Mathematics
DOI: 10.1016/j.dam.2011.07.018


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