I have a symmetric square matrix with elements from $\{0,1\}$. How can I block diagonalize it only swapping lines and columns or detect it's not possible?
2026-03-28 14:53:43.1774709623
Block diagonalization of a symmetric square boolean matrix
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I think this will work, if you are looking for an algorithm:
Start with a vertex.
Find all its neighbors $N_1$, and delete the vertex itself.
Find all the neigbors $N_2$ of the neigbors, and delete the neigbors $N_1$.
Continue the progress until no more neigbors are found.
Check if there is any vertex remained. If yes, then the matrix is block diagonisable; otherwise is not.