I don't know much (any?) graph theory, but I'm interested in learning a bit, and doing some calculations for a game. Is there a tool online where I could construct a graph (this one has 30-40 vertices, maybe 100 edges), and play around to explore its properties? Useful things to do would be describing paths, finding related paths, and letting me write formulas to calculate the value of a path.
(By contrast with Online tool for making graphs (vertices and edges)?, I'm not interested in the presentation, I'm interested in analysis, playing, exploring, manipulating, sharing...)