I have two graphs A,B each with 160 nodes but different labels. Each node has a position pos = (x,y,z) and an orientation (a1, a2, a3).
Now I want to find an optimal label matching of these two graphs. The graphs are obtained by a triangulation of the x and y coordinates (I am sure one can do better by leveraging the z coordinate, but this graph should suffice for now).
To give you a better intuition, here are the images of the graphs :
With which methods can I analyze the graphs and find an optimal matching (relabeling) such that similar nodes in graph A and graph B have similar position, orientation and graph properties like degree of the nodes.
I already tried to solve it with scipy.optimize as a linear programming problem (linear_sum_assignment(dist_nodes_A_to_B)) (dist_nodes_A_to_B is a 160x160 matrix containing the L2 distance of nodes i from A and j from B: dist_nodes_A_to_B[i,j]=sum(A.i.pos-B.j.pos)**2 )), but that yields inferior results.
Maybe the networkx library can help here, but I am not familiar with the library. I don't necessarily look for a concrete solution but rather for the name of algorithms which might help to solve the problem. If this question is inappropriate for SO, tell me where I can ask it.