In this study. the $ (h $-$ \varphi)_R $ and $ (h $-$ \varphi)_M $-contractions with two metrics endowed with a directed graph are examined using auxiliary functions. We propose a set of criteria that guarantees the existence of common fixed points for our contractions. This leads to a generalization of previous results in the literature. https://parisnaturalfoodes.shop/product-category/cal-mag-orange/