Regensburg 2019 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 16: Networks and Systemic Risks (joint SOE/DY)
SOE 16.1: Vortrag
Donnerstag, 4. April 2019, 09:30–10:00, H17
Large-deviation properties of random graphs — •Alexander K. Hartmann — University of Oldenburg
Distributions of the size of the largest component of the 2-core and of the graph diamater for Erdős-Rényi (ER) random graphs with finite connectivity c and a finite number N of nodes are numerically studied [1]. The distributions are obtained basically over the full range of the support, with probabilities down to values as small as 10−320. This is achieved by using an artificial finite-temperature (Boltzmann) ensemble. The distributions for the 2-core [2] resemble roughly the results obtained previously [3] for the largest components of the full ER random graphs, but they are shifted to much smaller probabilities (c≤ 1) or to smaller sizes (c>1). For the diameter [4], for values c<1, our results are in good agreement with analytical results. For c>1 the distribution is more complex and no complete analytical results are available.
For both cases, the numerical data is compatible with a convergence of the rate function to a limiting shape, i.e., the large-deviations principle apparently holds.
[1] A. K. Hartmann, Big Practical Guide to Computer Simulations, World-Scientific, Singapore (2015)
[1] A.K. Hartmann, Eur. Phys. J. Special Topics 226, 567 (2017)
[2] A.K. Hartmann, Eur. Phys. J. B 84, 627-634 (2011)
[3] A.K. Hartmann and M. Mézard, Phys. Rev. E 97, 032128 (2018)