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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...)

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What is the value of a path? (What is a "related" path?) – Qiaochu Yuan Jan 19 '11 at 23:12
Well, these are specific to the particular game I have in mind. But presumably there is a general principle of allocating values to edges and the value of the path thus being the sum of its edge values. Related path in this context means two paths that share a significant number of edges. "Significant" is something I'd like to define better...with the help of a graph analysis tool :) – Steve Bennett Jan 20 '11 at 7:29
How about software packages? Mathematica and Sage have graph theory functionality. Mathematica may be more user-friendly, Sage is open-source – Yaroslav Bulatov Jan 20 '11 at 8:26
For software you can download for free and run on your own computer and which is very flexible for drawing and getting insight about somewhat smaller sized graphs than what you mention you might try: – Joseph Malkevitch Feb 18 '12 at 15:50
I second the use of Sage. I use it for my research all the time. It has a lot of graph theory functions built in and you can write your own code if you want more. It's based on Python so you learn a useful programming language as you learn Sage. – Graphth Feb 19 '12 at 18:49

I coded up a thing called Graphrel for this sort of stuff. Currently it supports WYSIWYG editing and an interactive d3 forcelayout; also counts the number of vertices/edges, calculates connected components, as well as reflexivity/symmetry/transitivity etc. of its underlying relation. I'm still adding new features so feel free to make suggestions.

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For user friendly tool to play around the inputs nothing beats online Graph Theory tool under Wolfram Alpha in my opinion.

Wikipedia contains a large collection of Social network analysis softwares.

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