Using this definition of path, OP, you must realize that there may be exponentially (in the number of vertices + edges in the graph) many paths between two vertices (even in simple graphs).

For example, on this graph, the vertical axis goes up in steps of 2 degrees. Even though 7 degrees and 9 degrees are not shown, they are still represented between the labeled points.

This example also illustrates default pattern behavior with maps and explicit placement of the legend on the graph. It shows how the default solid map pattern rotates through every color in a colors ...