Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article, the δ-hyperbolic concept, originally developed for infinite graphs, is adapted to very large but finite graphs. Such graphs can indeed exhibit properties typical of negatively curved spaces, yet the traditional δ-hyperbolic concept, which requires existence of an upper bound on the fatness δ of the geodesic triangles, is unable to capture those properties, as any finite graph has finite δ. Here the idea is to scale δ relative to the diameter of the geodesic triangles and use the Cartan–Alexandrov–Toponogov (CAT) theory to derive the thresholding value of δdiam below which the geometry has negative curvature properties. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 157–180, 2008
['Edmond A. Jonckheere', 'Poonsuk Lohsoonthorn', 'Francis Bonahon']
I am writing a research paper on a idea Scaled Gromov hyperbolic graphs
[{"from": "human", "value": "I am writing a research paper on a idea Scaled Gromov hyperbolic graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article, the \u03b4-hyperbolic concept, originally developed for infinite graphs, is adapted to very large but finite graphs. Such graphs can indeed exhibit properties typical of negatively curved spaces, yet the traditional \u03b4-hyperbolic concept, which requires existence of an upper bound on the fatness \u03b4 of the geodesic triangles, is unable to capture those properties, as any finite graph has finite \u03b4. Here the idea is to scale \u03b4 relative to the diameter of the geodesic triangles and use the Cartan\u2013Alexandrov\u2013Toponogov (CAT) theory to derive the thresholding value of \u03b4diam below which the geometry has negative curvature properties. \u00a9 2007 Wiley Periodicals, Inc. J Graph Theory 57: 157\u2013180, 2008"}]