Generating random planar graphs where nodes have fixed coordinates

Is there a matlab code to generate random planar graphs where the position of nodes is fixed and only link connections change?

Answer 1

[Jaynik]

Hi Hari,

There is no direct function to generate random planar graphs with fixed nodes and changing edge connections. This task is a bit challenging and a basic approach to this problem would be as follows:

1. Start by defining the nodes in 2D space to create a planar graph.
2. We can use a known planar graph as a starting point.
3. Once we have a basic graph with us, we can rewire the edges randomly while checking for planarity.
4. The above step is just a naive way of changing the edges, if the graph is still planar, we move to some other edge, else we keep it as is and rewire some another edge.

This approach is quite basic and may not cover all scenarios effectively. A better approach can be given if you can share the problem in detail.

Hope this helps!