Advocate for 2nd neighbour included in graph triangulation

[KristinaUlicna]

I'm generating ground truth graphs from a random graph into which I drew 3 circle motifs. I noticed that although the graph has all objects stored with they respective object identities (code snippet):

grace/grace/simulator/simulate_graph.py

Lines 245 to 246 in a173bc3

	for node in motif:
	node.object_idx = n + 1

...the GT graph is not constructed correctly because some objects will form edges with the closeby noisy nodes due to the Delaunay triangulation:

Ground Truth Graph	Triangulated Graph

I think what would really help out here would be a different type of triangulation:

• hyperlinks to 2-hop neighbourhood,
• forming all edges below certain distance threshold,
• etc.

• Important for Generate the grace annotations automatically from the simulated image #152
• Mentioned in Advocate for 2nd neighbour included in graph triangulation #167

Perhaps this could be beneficial for the cross-over object connections.
@marjanfamili tagging you for further discussions.

[marjanfamili]

Are we looking at 3 intersecting circles here ?

if we add 2-hop neighbours, would this allow for more noise to enter the GT?
We could use higher-order Delauny triangulations?

[quantumjot]

You could also add the "flips":
https://en.wikipedia.org/wiki/Delaunay_triangulation#Visual_Delaunay_definition:_Flipping

[marjanfamili]

https://www.sciencedirect.com/science/article/pii/S092577210100027X

A second-order would achieve the flips I think