Let $A$ be a $d$-dimensional local ring containing a field. We will prove that the highest Lyubeznik number $\lambda_{d,d}(A)$ is equal to the number of connected components of the Hochster–Huneke graph associated to $B$, where $B=\widehat{\hat{A}^{\rm sh}}$ is the completion of the strict Henselization of the completion of $A$. This was proven by Lyubeznik in characteristic $p>0$. Our statement and proof are characteristic-free.