Let $M$ be a $0-1$ matrix.

Here a matrix has one component means we can traverse from a matrix entry $(i,j)$ which is $1$ to any other one by moving step of $(i\pm1,j),(i,j\pm1),(i\pm1,j\pm1)$ where each step you take you step on another $1$.

Can every $0-1$ be converted to a matrix of one component by permutations of rows and columns?

What if you only have steps $(i\pm1,j),(i,j\pm1)$?

What classes of matrices cannot have one component?

also posted: http://math.stackexchange.com/questions/1072461/connected-components-0-1-matrices