  We introduce a notion of doubly warped product of weighted graphs that is
consistent with the doubly warped product in the Riemannian setting. We
establish various discrete Bakry-\'Emery Ricci curvature-dimension bounds for
such warped products in terms of the curvature of the constituent graphs. This
requires deliberate analysis of the quadratic forms involved, prompting the
introduction of some crucial notions such as curvature saturation at a vertex.
In the spirit of being thorough and to provide a frame of reference, we also
introduce the $\left(R_1,R_2\right)$-doubly warped products of smooth measure
spaces and establish $\N$-Bakry-\'Emery Ricci curvature (lower) bounds thereof
in terms of those of the factors. At the end of these notes, we present
examples and demonstrate applications of warped products with some toy models.
