A graphical representation of a planar graph divides the plane into *regions* or *meshes* (as they are called in certain applications, e.g. in circuit theory).

Yes, the above fact is intuitive, but what I couldn't find in common textbooks on graph theory is a formal definition of mesh related to the definition of graph as a pair of sets of vertices and edges. In particular, is there a formal definition of mesh (or region) of a graph which does not rely on its graphical representation or which relies in a formalization thereof?