By [Gerschgorin's Circle Theorem][1], if the number of nonzero entries in each row is at most $d$, the spectral radius is at most $d$.  This bound is attained e.g. in a case where there are $d$ $1$'s  in each row and no $-1$'s, with eigenvector $(1,\ldots,1)^T$ for eigenvalue $d$.


 


  [1]: http://en.wikipedia.org/wiki/Gershgorin_circle_theorem