19. An ant moves along the edges of a unit cube at a speed of 1 unit per second, starting from any vertex. Assuming that each time the ant reaches a vertex, it turns to continue moving in any direction with equal probability (allowing for backtracking), the expected time for the ant to return to its starting point for the first time is $\qquad$
Consider the vertex sets $A=\{A\}, B=\left\{B_{1}, B_{2}, B_{3}\right\}$,
$$
C=\left\{C_{1}, C_{2}, C_{3}\right\}, D=\{D\}
$$

Considering the vertices and corresponding probabilities that the ant traverses starting from vertex $A$, let $E_{A}, E_{B}$, and $E_{C}$ represent the expected time for the ant to return to vertex $A$ for the first time when starting from vertices $A, B$, and $C$ respectively,

then we have $\left\{\begin{array}{l}E_{A}=E_{B}+1, \\ E_{B}=\frac{1}{3} \times 1+\frac{2}{3}\left(E_{C}+1\right), \\ E_{C}=\frac{2}{3}\left(E_{B}+1\right)+\frac{1}{3}\left(E_{C}+2\right)\end{array} \Rightarrow\left\{\begin{array}{l}E_{A}=E_{B}+1, \\ E_{B}=\frac{2}{3} E_{C}+1, \\ E_{C}=E_{B}+2\end{array} \Rightarrow\left\{\begin{array}{l}E_{A}=8, \\ E_{B}=7, \\ E_{C}=9 .\end{array}\right.\right.\right.$
In summary, the expected time for the ant to return to the starting point for the first time is 8.