Can anyone comment on the advantages and disadvantages of both graph theory vs. using a system of differential equations to study a complex network? For example, how much computing power and running time would a graph theory approach use compared to say solving a system of 100 differential equations? Memory space? How about the ability to add data or new equations on the fly (thinking of data structures, linked lists)? Example, let's just say I had a large network of pipes and wanted to see if water got from point A to point B (all the way at the end) and at what rate. What would happen if a certain node where pipes meet got knocked out? Would water still get to B? These are some of the types of questions I'm interested in. I'm just wondering if one decided to model such a network, which methods used would be more efficient, still provide powerful analysis and good results.