  We investigate symmetry of the silting quiver of a given algebra which is
induced by an anti-automorphism of the algebra. In particular, one shows that
if there is a primitive idempotent fixed by the anti-automorphism, then the
2-silting quiver ($=$ the support $\tau$-tilting quiver) has a bisection.
Consequently, in that case, we obtain that the cardinality of the 2-silting
quiver is an even number (if it is finite).
