Like I've said before I'm no mathematician, but according to This Website amoung others "For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge"

Also per wikipedia : "In graph theory, a graph consists of a set of connections between objects. Each object is a vertex. Each connection, between two vertices, forms an edge, or arc "

So wouldn't a line connecting two vertices on a sphere be considered an edge or arc?

Of course does this mathematical definition of an edge have any meaning in reference to the "edge" of the universe?