  A family of subsets $\mathcal{F}$ is intersecting if $A \cap B \neq
\emptyset$ for any $A, B \in \mathcal{F}$. In this paper, we show that for
given integers $k > d \ge 2$ and $n \ge 2k+2d-3$, and any intersecting family
$\mathcal{F}$ of $k$-subsets of $\{1, \cdots, n\}$, there exists a $d$-subset
of $[n]$ contained in at most $\binom{n-d-1}{k-d-1}$ subsets of $\mathcal{F}$.
This result, proved using spectral graph theory, gives a $d$-degree
generalization of the celebrated Erd\H{o}s-Ko-Rado Theorem, improving a theorem
of Kupavskii.
