D3 Plus Ring Network Cutoff

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I'm using d3plus to produce ring charts, for example the simple ring shown here (http://d3plus.org/examples/d3plus-network/simple-rings/).

My problem is that the rings I'm producing have a lot of connections at the secondary level, which makes the ring look entirely to busy.

Ring Example I produced:

Ring Example I produced

The structure of my data is a simple link data set

links = [{source: "A", target: "B", strength: SomeNumber },....]

I've read down through the documentation, but I'm at a complete loss as to how to minimize the number of connections shown on the tertiary level.

There must be something I'm missing, I would like to cut-off the number of links shown by only showing (at maximum) the top two or three targets to the source at the second level for example.

Just hoping somebody here has some ideas about it.

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