We generated hyperedges following the process in M. Leodeanu et al. (2012).

We consider 150 points on the space [-.5,.5]x[-.5,.5] such that:

Nodes 0-29:  noisy points on a line A with slope -1
Nodes 30-59: noisy points on a line B with slope 0.02
Nodes 60-99: noisy points on a line C with slope 0.8
Nodes 100-159: random points

We sample points in sets of 3 and 4 respecteivly, keeping
groups of points that are well-aligned (w.r.t. residuals
of the numpy.polyfit() function).
The hyperedges retained are given in the supplied files:

  hypergraph_3uniform.csv: 159,816 3-edges
  hypergraph_4uniform.csv: 160,000 4-edges

To generate our plots, we randomly sampled from those sets
with respect to 3 different regimes:

- same proportion of 3 and 4-edges
- 2/3 3-edges, or
- 2/3 4-edges

and we also sample such that we have roughly twice as many edges 
all coming from the same line (A, B or C) as we have sets with 
mixed lines and/or random points.


