Online tool for making graphs (vertices and edges)?

For drawing graph, the best is TIKZ but it does take some time to study, an alternate is graphviz

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Rollbacked:

For drawing 2D geometry, try GeoGebra or Sketchpad (licensed).

For drawing 3D geometry, try Cabri 3d (licensed).

yEd is a free cross-platform application that lets you interactively create nodes and edges via drag and drop, format them with different shapes and styles, and apply various graph layout algorithms to arrange the graph neatly.

http://illuminations.nctm.org/ActivityDetail.aspx?ID=20 In the above link you can have a tool where you can draw graphs, check degree, find eulerian path, hamiltonian path.