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And instead of saying "there are three links from this node to that
node" I would instead say "there is one link from this node to that
node, and it has these three supported options".  I think that I would
perform the three operations in parallel on the set of existing states
and then strip out the results which achieved an invalid state.
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perhaps the adjacency matrix is not the way to go but you
could use this and just have a link information list of boxed items
with multiple items for multiple links.
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Thank you, Devon and Raul.

In addition to having multiple links between the same nodes, and having data 
associated with a link, I also want to find "preceeding" and "following" nodes 
from a given node in a constant time. So, I don't think array of links would 
work there.

(Fortunately, my graph is always connected - so, link array does mention all 
existing nodes, i.e., there are no nodes having no incoming or outgoing links.)

Now, a typical procedure which I do on this graph is "from this node N, find 
all (directed) sequences of links of length L". "Directed" means that in graph 
2->3->4 sequence (2-3-4) is directed, since "beginning" of the arrow always 
starts where is the "end" of previous arrow in the sequence. Sequence (2-3-2) 
isn't directed in this sense. Since it's DAG, a node can't happen twice in the 
same sequence.

Alexander
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