  For a simple graph $\Gamma$ and for unital $C^*$-algebras with GNS-faithful
states $(\mathbf{A}_v,\varphi_v)$ for $v\in V\Gamma$, we consider the reduced
graph product $(\mathcal{A},\varphi)=*_{v,\Gamma}(\mathbf{A}_{v},\varphi_v)$ ,
and show that if every $C^*$-algebra $\mathbf{A}_{v}$ has the completely
contractive approximation property (CCAP) and satisfies some additional
condition, then the graph product has the CCAP as well. The additional
condition imposed is satisfied in natural cases, for example for the reduced
group $C^*$-algebra of a discrete group $G$ that possesses the CCAP.
  Our result is an extension of the result of Ricard and Xu in [Proposition
4.11, 25] where they prove this result under the same conditions for free
products. Moreover, our result also extends the result of Reckwerdt in [Theorem
5.5, 24], where he proved for groups that weak amenability with
Cowling-Haagerup constant $1$ is preserved under graph products. Our result
further covers many new cases coming from Hecke-algebras and discrete quantum
groups.
