Random rectangular graphs

Ernesto Estrada, Matthew Sheerin

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13 Citations (Scopus)
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Abstract

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0, 1]2 . The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b = 1/a, and the radius r used to connect the nodes. When a = 1 we recover the RGG, and when a → ∞ the very elongated rectangle generated resembles a one-dimensional RGG. We obtain here analytical expressions for the average degree, degree distribution, connectivity, average path length and clustering coefficient for RRG. These results provide evidence that show that most of these properties depend on the connection radius and the side length of the rectangle, usually in a monotonic way. The clustering coefficient, however, increases when the square is transformed into a slightly elongated rectangle, and after this maximum it decays with the increase of the elongation of the rectangle. We support all our findings by computational simulations that show the goodness of the theoretical models proposed for RRGs.
Original languageEnglish
Article number042805
Number of pages9
JournalPhysical Review E
Volume91
Issue number4
DOIs
Publication statusPublished - 21 Apr 2015

Keywords

  • random geometric graph
  • rectangle length
  • clustering coefficient
  • path length

Cite this

Estrada, E., & Sheerin, M. (2015). Random rectangular graphs. Physical Review E, 91(4), [042805]. https://doi.org/10.1103/PhysRevE.91.042805