Ross Kirsling's D3.js-based Directed Graph Editor is a simple and convenient online graph editor. It doesn't include weighted edges, but it probably wouldn't be difficult to add that capability if you're willing to learn D3.js. (OK, learning D3.js's weird conceptual model is necessarily a trivial project, even for experienced programmers). Kirsling's graph editor also lacks other fancy features that some of the tools listed here include. However, it's right there online, and it might be one needs for many purposes. Kirsling's graph editor is part of his Modal Logic Playground.
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