So I've got this thing working, using the ideas presented by @recursiverecursion.
This is how I did it (I chose R=15 as the nodes have a radii of 10, which would ensure that the lines started from a point _outside_ the nodes, as per my figure.
$$ \theta = arctan(\frac{y_0-y_1}{x_0-x_1})\\\ \Delta x = R * cos(\theta)\\\ \Delta y = R * sin(\theta)\\\ $$
Then I drew a line from $(x_o + \Delta x, y_0-\Delta y)$ to $(x_1 - \Delta x, y_1+\Delta y)$. Worked splendidly :-)