Shawn, this I'm not completely happy with :
Now, how do we draw edges on this network? For every person, we connect their childhood Family node to their adult Family node (if they ever marry/have children).
I agree each person appears as a child in at most one Family node (the node of her parents), but she can appear in several nodes as parent is she has mutiple unions. So, it should be "adult Family node(s)".
If people are edges, the simple connection rule should be : there is an edge linking two Family nodes if they have a common member. This would settle nicely the case of multiple unions and half-siblings.
Node 1 : parents John and Mary, 2 children Jane and Paul.
Node 2 : parents Fred and Mary, 1 child Debbie.
Node 3 : Fred and Jenny, 2 children Pat and Julie.
There is an edge between N1 and N2 (Mary), and an edge between N2 and N3 (Fred). N1 and N3 are at distance 2. That way half-siblings belong to nodes at distance 1, full siblings belong to the same node.