[Crunch]

In a weighted Adjacency Matrix representation What does 0 and infinity mean?

[r.stiltskin]

You're probably not going to like this answer, but I'd say they mean whatever you want them to mean. A graph is an abstraction used to model some underlying relationship, process, etc. Weights on the edges of a weighted graph only have meaning in that context. They might represent some measure of cost of traversing the edge, in which case 0 would indicate the best kind of edge in some sense and ∞ would indicate an edge of "infinite" cost, or essentially a "non-edge". But conversely, the weights might be a measure of the rate of flow that each edge can accomodate, in which case 0 would be a "non-edge" and ∞ would represent an ideal edge that can handle unlimited traffic. It all depends on what the graph is modeling.