If I have an adjacency matrix like this (for example): $$\begin{bmatrix}0 &1& 2& 2& 0& 1\\ 0 &0 &2 &2 &2 &1\\ 2 &2 &2 &2 &1 &2\\ 2 &2 &2 &0 &2 &2\\ 0 &1 &2 &2 &0 &1\\ 1 &1 &2 &2 &1 &0\end{bmatrix}$$
0 = connections 1 = red edge 2 = blue edge
Then how would I go about verifying if there is a monochromatic $K_{10}$ in it? Note: I will have to apply it to very large graphs.
I would like an algorithm, but if anyone has a python library or a framework in another language which is able to verify this let me know please.
You can split into two graphs (red and blue), and independently look for a maximum clique in each, stopping whenever you reach $10$ in either graph.
As a preprocessing step in each graph, you can recursively remove any nodes with degree $<9$.
See Solving the maximum clique and vertex coloring problems on very large sparse networks.