Defining a graph with both vertex cost and edge cost

Question

In general, a graph with cost value assigned on edges can be defined as $G=(V,E,c)$ where $c:E\rightarrow\mathbb{R}$ is the edge cost function. But, what about a graph with cost value assigned on both edges and vertices? Is there any formal mathematical structures to define it? Is there any source/literature that discuss about such graph?