This concerns graphs that are sets of vertices and edges G={V,E}, not graphical depiction of functions.
Imagine a graph that is a 2D square mesh of vertices. Such a graph can be constructed, for example, by taking typical graph paper, mapping a vertex to each intersection of lines, and an edge to each line segment. The graph paper is thus a visual representation of an abstract graph G. While the visual artifact has spatial attributes (lengths of edges, angles between any three vertices, etc.), G has none of this, only the set of vertices and the set of edges.
Now in the absence of spatial reference, a graph thus derived will have some properties of interest. Most vertices will have 4 neighbors, in fact if V and E are allowed to be infinite, all will have 4 neighbors. And the graph will have planarity. I'm specifically interested in this kind of graph, I.e. ones that have the same properties one would get for those constructed by "copying a 2D mesh". (distinct from the family of graphs that are simply described by "each vertex has 4 neighbor", which could be non planar as the diamond lattice for example)
Is it correct to call the abstract graph G a "2d mesh", or is their a more appropriate name for this construct when explicit spatial attributes are excluded? Question generalizes for "2D triangular mesh", "2D hexagonal mesh".