Generating random connected planar graphs

Abstract

Connected planar graphs are of interest to a variety of scholars. Being able to simulate a database of such graphs with selected properties would support specific types of inference for spatial analysis and other network-based disciplines. This paper presents a simple, efficient, and flexible connected planar graph generator for this purpose. It also summarizes a comparison between an empirical set of specimen graphs and their simulated counterpart set, and establishes evidence for positing a conjecture about the principal eigenvalue of connected planar graphs. Finally, it summarizes a probability assessment of the algorithm’s outcomes as well as a comparison between the new algorithm and selected existing planar graph generators.

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Notes

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    This upper bound on n is a restriction set by the Fortran compiler used. It can be relaxed by changing the computer software for implementation (see supplementary material for the Fortran code).

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Acknowledgments

Dr. Daniel A. Griffith is an Ashbel Smith Professor of Geospatial Information Sciences.

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Griffith, D.A. Generating random connected planar graphs. Geoinformatica 22, 767–782 (2018). https://doi.org/10.1007/s10707-018-0328-3

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Keywords

  • Adjacency matrix
  • Connected graph
  • Planar graph
  • Random sampling