I have a matrix $A \in \{0,1\}^{n \times n}$ -- i.e. a matrix with 1s and 0s only.
Is there a way to find or upper bound its largest eigenvalue?
I have a feeling it is related to connectivity of directed graphs, if $A$ is thought of as adjacency matrix.
Also, when trying
A = rand(10,10); A = A <= p; [x,S] = eig(A+0.00); S(1,1)
in Matlab for various values of p (0.1,0.2,...) (many times) it seems like S(1,1), the largest eigenvalue, is around 1/p.
Any help is appreciated.