(Not too off topic I hope?) problem

[Duncan Smith]

I am trying to get an MCMC algorithm (based on a tree structure) implemented
/ prototyped in Python.  I have a problem figuring out how to efficiently
randomly select a tree edge (ie. with prob = 1/(n-1)) when the tree is a
dictionary {node: [adjacency list], ...}.  If I randomly select a node and
then an adjacent node, the probability of selecting the edge (defined by the
pair) depends heavily on the tree structure.  The solution I currently have
is potentially less efficient than generating all the edges from the
dictionary and selecting one at random.  Any ideas.  Thanks in advance.

Duncan