Graph Drawing With Weighted Edges

Question

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.

Answer 1

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?

Answer 2

Many graph/network layout algorithms are implicitly capable of handling weighted networks, but you may need to do some pre-processing and tweaks to the implementation to get it to work. Usually the first step is to determine if your weights represent "similarities" (usually interpreted to mean that stronger weights should place nodes closer togeter) or "dissimilarities" (stronger weights = father apart). The most common case is the former, so you will need to translate them to dissimilarities, often done by subtracting each edge value from the maximum observed edge value in the network. The matrix of dissimilarity values for each edge can then be fed to the algorithm and interpreted as desired distances in the layout space for each edge (ie "spring lengths")--usually after multiplying by some constant to transform to display units (pixels).

If you tell me what language you are using, I may be able to point you to some code examples.