Hi Simone,

answering briefly below:

Vertex is something we can safety drop because we
know its nature at priori, markers are unnecessary.This is fine.

+1.

what is the sense, at that point, on keeping the Edge?!! It would be
more than enough to know which is the Head and which is the Tail in
the Edge to get the W!

good observation. My 2 cents: it might still make sense for users to map their existing domain (including "edges") to the graph (e.g. Routers to Vertices and Cables to Edges) and "get it back" as soon as they are done with graph operations (e.g. once they find the shortest path, they automatically have the sequence of Cables they need).

maybe because they implement OrderedMonoid? :)
[...]
how much would Addition and Multiplication interface differ each other?
[...]
that would be fine, what is not clear is that Monoids expose the same
interface, so *Operations class implementation canot declare same
method multiple times

answering all the above: that is another reason why I would like our current Monoid to be called Addition (and Addition#sum instead of Monoid#append, etc), so that it is semantically clearer and later we can introduce Multiplication as a completely independent interface.

enough talk IMHO, time to code and make concrete proposals

Sure!
I'll play with weights first, because I already know what I want to do.
As for Vertex/Edge markers I still see valuable feedback coming in, so I'll wait a bit.

Branching is ok -- especially for the second part which sounds like a real earthquake ;)

Ciao,
Claudio

--
Claudio Squarcella
PhD student at Roma Tre University
http://www.dia.uniroma3.it/~squarcel
http://squarcella.com/


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