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For any $r$-order $\{0, 1\}$-tensor $A$ with $e$ ones, we prove that thespectral radius of $A$ is at most $e^{\frac{r-1}{r}}$ with the equality holdsif and only if $e={k^r}$ for some integer $k$ and all ones forms a principalsub-tensor ${\bf 1}_{k\times \cdots \times k}$. We also prove a stabilityresult for general tensor $A$ with $e$ ones where $e=k^r+l$ with relativelysmall $l$. Using the stability result, we completely characterized the tensorsachieving the maximum spectral radius among all $r$-order $\{0, 1\}$-tensor $A$with $k^r+l$ ones, for $-r-1\leq l \leq r$, and $k$ sufficiently large.

Spectral Radius of $\{0, 1\}$-Tensor with Prescribed Number of Ones