I have a binary adjacency matrix $M$ of size $72\times 72$. I would like to find all possible combinations of 18 non-adjacent nodes.
There are $^{72}C_{18}$ possible (adjacent and non-adjacenct) combinations. I want to find all valid combinations.
You can try the adjacency matrix at: How to color nodes in a adjacency graph with different colors?
If one particular node is in a valid combination, then its adjacent nodes cannot be part of that valid combination.
I am using the following code.
all = FindIndependentVertexSet[AdjacencyGraph@M, {18, Infinity}, All];
Union @ Catenate @ Map[Subsets[#, {18}]&] @ all
The Mathematica kernel keep running........
Is it possible to find them in an efficient manner.