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I am interested in a certain class of directed hypergraphs, more precisely in the class of those hypergraphs each of whose hyperedges contain an even number of nodes (not necessarily the same even number for each hyperedge!), the half of which are "initial nodes" and the other half being "terminal nodes".

This is admittedly a strong condition, but at least directed graphs are a special case of hypergraphs with said property. Has this class already been studied? Does it have a name?

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If you drop the even-ness condition then you just have what is called an "oriented hypergraph": I first came across them in the recent work of Rusnak but they've probably appeared in the literature well before that, possibly wth a different name. In any case, here is a reference with definitions and basic properties:

http://arxiv.org/pdf/1210.0943v1.pdf

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  • $\begingroup$ thanks. but i was looking exactly for a refinement of rusnak's concepts. in my post, i used the word "directed" as a sloppy synonym of your "oriented". it was the further condition the one that really matters. $\endgroup$
    – Delio Mugnolo
    Commented Apr 16, 2014 at 23:07

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