Minimum spanning tree problem

Does anyone know of a quick efficient way of both keeping track of the number of arcs (connections) each node has (and preferably to which other nodes it is connected). And a way of detecting if a "circuit" has been formed within a group of nodes.

I need to be able to do this in both VB and C.

I'm having trouble storing both the numerous nodes and the seemingly limitless potential connections!

Any ideas?

the first can be done with doublelinked network datastructures in c++, in vb you can use a collection object, this is of course, if you assume speeed is unimportant. Otherways you could do something similar even with UDT's. The second is done with a graph search algoritm