  We consider the notion of discrete Ricci curvature for graphs defined by
Schmuckenschl{\"a}ger \cite{shmuck} and compute its value for Bruhat graphs
associated to finite Coxeter groups. To do so we work with the geometric
realization of a finite Coxeter group and a classical result obtained by Dyer
in \cite{Dyer}. As an application we obtain a bound for the spectral gap of the
Bruhat graph of any finite Coxeter group and an isoperimetric inequality for
them. Our proofs are case-free.
