Nested hierarchies in planar graphs

Won Min Song; T. Di Matteo; Tomaso Aste

doi:10.1016/j.dam.2011.07.018

Nested hierarchies in planar graphs

Won Min Song^*, T. Di Matteo, Tomaso Aste

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2135-2146
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	159
Issue number	17
DOIs	https://doi.org/10.1016/j.dam.2011.07.018
Publication status	Published - 28 Oct 2011

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10.1016/j.dam.2011.07.018

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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.",

keywords = "3-clique, Bubble, Community, Hierarchy, Maximal planar graph",

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AU - Song, Won Min

AU - Di Matteo, T.

AU - Aste, Tomaso

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AB - 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.

KW - 3-clique

KW - Bubble

KW - Community

KW - Hierarchy

KW - Maximal planar graph

UR - https://www.scopus.com/pages/publications/80052603806

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DO - 10.1016/j.dam.2011.07.018

M3 - Article

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VL - 159

SP - 2135

EP - 2146

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 17

ER -

Nested hierarchies in planar graphs

Abstract

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