J A S O N B E H R S T O C K
	The following applet, written by Christopher Manning, allows you to visualize random graph as you vary the vertex count and density: Some papers I've recently written which involve random graphs are: A threshold for relative hyperbolicity in random right-angled Coxeter groups, with A. Ciceksiz and V. Falgas-Ravry Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups, with V. Falgas-Ravry and T. Susse Random Structures and Algorithms, vol. 60, 594-640, 2022. Global structural properties of random graphs, with V. Falgas-Ravry, M. Hagen and T. Susse International Mathematics Research Notices, vol. 2018, 1411-1441, 2018. Thickness, relative hyperbolicity, and randomness in Coxeter groups, with M. Hagen and A. Sisto, with an appendix written jointly with P.-E. Caprace Algebraic & Geometric Topology, vol. 17, 705-740, 2017. I've developed some programs with my collaborators for experimenting with graphs. These program allow one to input a graph (or set of graphs) or enter parameters for the creation of a random graph; then it tests the graphs for each of these properties: AS checks for being an "augmented suspension". CFS checks for having the "constructed from squares" property. LGT checks whether or not a graph yields a relatively hyperbolic right-angled coxeter group. TEA, was written by Robbie Lyman, and computes upper bounds on the order of thickness of the right-angled Coxeter group associated to a graph. Details about his program are available in his undergraduate thesis, which I supervised, Algorithm computations of thickness in right-angled Coxeter groups The following diagram (using data from the program CFS) shows a sharp transition at density cn^-1/2 in the probability of a random graph being CFS. The movie below shows the prevalence of thickness in random right-angled Coxeter groups; data for this movie was computed using TEA. Please send any feedback or questions about the software to me at: jason.behrstock@lehman.cuny.edu

J A S O N B E H R S T O C K

The following applet, written by Christopher Manning, allows you to visualize random graph as you vary the vertex count and density:

Some papers I've recently written which involve random graphs are:

A threshold for relative hyperbolicity in random right-angled Coxeter groups, with A. Ciceksiz and V. Falgas-Ravry
Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups, with V. Falgas-Ravry and T. Susse
Random Structures and Algorithms, vol. 60, 594-640, 2022.
Global structural properties of random graphs, with V. Falgas-Ravry, M. Hagen and T. Susse
International Mathematics Research Notices, vol. 2018, 1411-1441, 2018.
Thickness, relative hyperbolicity, and randomness in Coxeter groups, with M. Hagen and A. Sisto, with an appendix written jointly with P.-E. Caprace
Algebraic & Geometric Topology, vol. 17, 705-740, 2017.

I've developed some programs with my collaborators for experimenting with graphs. These program allow one to input a graph (or set of graphs) or enter parameters for the creation of a random graph; then it tests the graphs for each of these properties:

AS checks for being an "augmented suspension".
CFS checks for having the "constructed from squares" property.
LGT checks whether or not a graph yields a relatively hyperbolic right-angled coxeter group.
TEA, was written by Robbie Lyman, and computes upper bounds on the order of thickness of the right-angled Coxeter group associated to a graph. Details about his program are available in his undergraduate thesis, which I supervised, Algorithm computations of thickness in right-angled Coxeter groups

The following diagram (using data from the program CFS) shows a sharp transition at density cn^-1/2 in the probability of a random graph being CFS.

The movie below shows the prevalence of thickness in random right-angled Coxeter groups; data for this movie was computed using TEA.

Please send any feedback or questions about the software to me at: jason.behrstock@lehman.cuny.edu