I seem to be running into some limits with the HUGIN software. What is the maximum number of nodes and edges that HUGIN can handle?
There are no built-in limits on the number of nodes or the number of edges. The amount of memory (RAM) in your computer determines how complex your models can be (except that since Hugin is currently a 32-bit application, at most 4GB can be utilized).
The most important cause for excessive memory usage is a model that is very densely connected. For example, a completely connected network with 30 binary nodes would create a junction tree with a single clique, and the state space of that clique would be of size 2^30. Since each element of that state space has a floating-point value (representing the probability) of type "double" (occupying 8 bytes in the computer memory) associated with it, such a clique would occupy 8GB of memory.
On the other hand, a network that is a tree (that is, there is only one path between any two nodes) will only use memory proportional to the number of nodes and the largest conditional probability table. If your network is a tree (or "almost" a tree), then you should be able to have at least 10000 and maybe even 100000 nodes.