Your question is a bit vague, you mean edges inside a mesh or edges
between meshes ?

if your question is the latter i would say that an edge connects 2
meshes

given this structure you may employ graph navigation algorithm to
select the shortest path between meshes and other algorithms as well, it
depends of what you need

I am reading up and am interested in using mesh navigation graphs for path finding.

Given that each mesh represents a node on the navigation graph, what are the edges of the mesh navigation graph?

Also, how are the edge costs of the mesh navigation graph computed?

The diagrams I have seen show the meshes lying adjacent to one another with no edges, unlike the waypoint navigation graph.