By Gerschgorin's Circle Theorem, 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 $d$.
Robert Israel
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