Nested hierarchies in planar graphs |
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| Authors: | Won-Min Song T. Di Matteo Tomaso Aste |
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| Affiliation: | a Applied Mathematics, Research School of Physical Sciences, The Australian National University, 0200 Canberra, Australiab Department of Mathematics, King’s College, The Strand, London, WC2R 2LS, UKc School of Physical Sciences, University of Kent, CT2 7NZ, UK |
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| Abstract: | 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 hierarchical relations between these communities. |
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| Keywords: | Maximal planar graph 3-clique Bubble Hierarchy Community |
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