Unimodular lattice triangulations as small-world and scale-free random graphs

Journal article

Publication Details

Author(s): Mecke K, Krüger B, Schmidt E
Journal: New Journal of Physics
Publication year: 2015
Volume: 17
ISSN: 1367-2630


Real-world networks, e.g., the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and one-dimensional simplices with edges. Since these triangulations are ergodic with respect to a certain Pachner flip, applying different Monte Carlo simulations enables us to calculate average properties of random triangulations, as well as canonical ensemble averages, using an energy functional that is approximately the variance of the degree distribution. All considered triangulations have clustering coefficients comparable with real-world graphs; for the canonical ensemble there are inverse temperatures with small shortest path length independent of system size. Tuning the inverse temperature to a quasi-critical value leads to an indication of scale-free behaviour for degrees k >= 5. Using triangulations as a random graph model can improve the understanding of real-world networks, especially if the actual distance of the embedded nodes becomes important.

FAU Authors / FAU Editors

Krüger, Benedikt
Lehrstuhl für Theoretische Physik
Mecke, Klaus Prof. Dr.
Lehrstuhl für Theoretische Physik
Schmidt, Ella
Professur für Allgemeine Mineralogie/Kristallographie

How to cite

Mecke, K., Krüger, B., & Schmidt, E. (2015). Unimodular lattice triangulations as small-world and scale-free random graphs. New Journal of Physics, 17. https://dx.doi.org/10.1088/1367-2630/17/2/023013

Mecke, Klaus, Benedikt Krüger, and Ella Schmidt. "Unimodular lattice triangulations as small-world and scale-free random graphs." New Journal of Physics 17 (2015).


Last updated on 2018-19-04 at 04:10