Nested hierarchies in planar graphs
Geometric Topology
2011-10-18 v1
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
Cite
@article{arxiv.0906.4826,
title = {Nested hierarchies in planar graphs},
author = {Won-Min Song and T. Di Matteo and Tomaso Aste},
journal= {arXiv preprint arXiv:0906.4826},
year = {2011}
}