A self study course I can recommend for topology is Topology by JR Munkres followed by Algebraic Topology by A Hatcher (freely and legally available online, courtesy of the author!). But that is if you want to be able to really do the math in all its glorious detail. Basic Topology by MA Armstrong is a shortcut and a very good one at that.
The closest I can get to what you are asking for here is Network Topology. Is that what you mean? In that case you should be probably be looking at topological graph theory. Wikipedia also tells me that something called Computational Topology exists, but that is probably not what you are looking for.