  We propose a simple and generic holographic $c$-function that is defined
purely from geometry by using the non-affine expansion for null congruences. We
examined the proposal for BPS black solutions in $\mathcal{N}=2$ gauged
supergravity that interpolate between two different dimensional AdS spacetimes
and also for domain wall solutions. Moreover, we commented on the relation of
this geometric proposal with the one from the holographic entanglement entropy.
