I'm learning as I go, so I'll have to take your word for it.

The reason why the mesh does not exist at the centre is because that's where the black hole is.

In Quantum Graphity, the black hole is made up of a complete graph, like in the attached image. The complete graph + the exterior graph produces the spatial portion of gravitation.

My theory is that the edges are directed, oscillating between back and forward (very fast, at the Planck frequency right next to the event horizon), causing gravitational time dilation. Alternatively, one can consider the vertices to be the oscillators, forming gradients along the edges. Either way, this would be the temporal part of gravitation.

Both space and time are curved.

Right now my propagators move by picking an edge to follow in a pseudorandom fashion. This can't be the full story though, since the gradient of gravitational time dilation should affect propagators -- pseudorandom propagators don't respond to temporal gravitation, only respond to spatial gravitation. I'm working on it... I'm envisioning a scattering matrix that is n*n in size, where n is the number of edges for a particular vertex.

Does it make sense?

The reason why the mesh does not exist at the centre is because that's where the black hole is.

Yes. However, the "dual" of a Delaunay triangulation is the Voronoi tesselation, and it covers the entire space. If it doesn't, it's not a Voronoi tesselation, and thus not the dual of the Delaunay triangulation.
You can call it something else, like "supported cell area" and you'll be fine :-)

Ok.

In the meantime, I've tried to model the black hole's exterior region using triangles or hexagons (mostly).

Here are the important properties of the images attached below.

image 1

Excuse me,

why is this problem being discussed in Multiplayer and Network sub-forum?

Networks are sometimes modeled by graph theory. One of the next steps is to put in a hopping entity that travels through the network (graph).

About those last 4 images:

Since the pointing outward value for all 4 solutions doesn't ever get to 0.5 and beyond (red lines don't ever become as prevalent as blue lines), the black hole's exterior network produces attraction via spatial curvature.

The average dot product value shows that the blue and red lines are almost always pointing nearly orthogonal to the corresponding outward pointing normals (not shown)... like there are layers of rotation.

The red lines along the black hole surface should actually be pointing inward when the black hole interior is modelled by a complete network (not shown). Ignore those red lines, they should be blue.

The PDF is at http://vixra.org/abs/1601.0066 (4.1 MB)

A 3D Delaunay tetrahedralization: