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I'm looking to build an algorithm (or reuse one) that organizes nodes and edges on a 2 dimensional canvas where edges can have corresponding weights.

Any starting material and info would be helpful.

A: 

What would the weights do to affect their placement on your canvas?

That being said, you might want to look into graphviz and, more specifically, the DOT language, which organizes nodes on a canvas.

Many graph visualization frameworks use a force-based simulation, in which all nodes exert a repulsive force against each other (with their mass being their size), and edges exert tension on the nodes they connect. This creates aesthetically-arranged graph visualizations.

Although again, I'm not sure where you want node "weights" to come into play. Do you want weighted nodes to be more in the center? To be larger? More further apart?

Justin L.