Block-diagonalize matrix based on specific block criteria

I would like to re-arrange a symmetric logical matrix to form "blocks" along the diangonal. Here, I define these blocks based on row/colums that share ones.

To illustrate visually, here is the inital symmetric logical matrix:

And I would like to find the permutations that give me this:

[Bruno Luong]

And the "specific block criteria" is exactly what?

Answer 1

[Bruno Luong]

See symrcm symamd colamd commands and such

[Ludovic Tenorio]

symrcm seems to have done the job, thank you