## Layered Graph Drawing (The Sugiyama Method)

September 28, 2011 § Leave a comment

There are various graph drawing conventions and aesthetics. Consider a digraph, we would like:

- Edges roughly pointed in one direction
- a. Nodes evenly distributed

b. Long edges avoided. - Edge Crossing Minimized.
- Edges should be as straight / vertical as possible.

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The Sugiyama Method aims to address these conventions, and is useful for dependency diagrams, flow diagrams, conceptual lattices and other directed graphs. Essentially, layered networks are useful in representing Dependency relations.

The Sugiyama Method:

- Cycle Removal

– may temporarily Reverse some edges

– each cycle must have at least one edge against the flow (NP Hard), requires heuristic (e.g. enhanced greedy heuristic) or Randomized Algorithms. - Layering. (assigning y)

– vertices may be introduced to split edges - Node Ordering

– the Ordering is all that matters (not co-ordinates), NP Hard.

– Many heuristics. e.g. Layer-by-layer sweep (two-layer crossing problem), addressed by 1. Sorting, 2. Barrycentre, or 3. Median, methods. - Co-Ordinate Assignment.

Slides on this topic can be found here.

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