Modeling a completely connected graph in Alloy
alloy, logic, model-checking
Solution
How about
adj = Node -> Node - iden
This basically says that `adj` contains all possible pairs of nodes, except identities (self-loops).
The reason why it is ok that `Node1` and `Node2` are not connected for your model is the last clause of your fact which constrains that for each node, all nodes are transitively reachable, but it seems to me that you want them to be immediately reachable. Alternatively to using my solution above, you can change
`all n: Node | Node in n.*adj` to `all n: Node | (Node - n) in n.adj`
to get the same effect.
Problem
I'm trying to get my feet wet with Alloy (also relatively new-ish to formal logic as well), and I'm trying to start with a completely connected graph of nodes. ``` sig Node { adj : set Node } fact { adj = ~adj -- symmetrical no iden & adj -- no loops all n : Node | Node in n.*adj -- connected } pred ex { } run ex for exactly 3 Node ``` As you can see from the image, Nodes 0 and 1 aren't connected. I thought that my fact was enough to make it completely connected...but perhaps I missed something.