کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
418551 | 681684 | 2011 | 12 صفحه PDF | دانلود رایگان |

We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph GG and defines a unique hierarchy. We demonstrate that GG is the union of a set of special subgraphs, named ‘bubbles’, that are themselves maximal planar graphs. The graph GG 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 GG into communities and the tree structure defines the hierarchical relations between these communities.
► We construct unique hierarchies on a maximal planar graph.
► Separating property of cycles defines a partial order on the set of 3-cliques.
► The poset defines a complete set of special subgraphs called ‘bubbles’.
► The bubbles and separating 3-cliques constitute a unique bubble hierarchical tree.
► Communities and hierarchy naturally emerge from the bubble hierarchy.
Journal: Discrete Applied Mathematics - Volume 159, Issue 17, 28 October 2011, Pages 2135–2146