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As will be apparent, my familiarity with graph theory is somewhat limited; I haven't been able to find a reliable answer to this question, which may well be incorrect phrasing on my part. My question is as follows:

If I have two nodes, n1 and n2, connected by an edge e1,2. Now I introduce a third node, n3 with a single edge, e3. Is it possible for this edge, with directionality, to 'point' to the edge e1,2? That is, 'activation' of n3 would alter the weight of e1,2 via e3?

Basically, I am trying to conceptualise a model in which the 'activation' of one property (n3) influences the extent to which another property (n1) influences (via e1,2) yet another property (n2). The only way I can envision that is through an edge (e3) 'pointing at' another edge (e1,2). That way, activation of n3 would alter the weighting on e1,2, and therefore alter how n1 activates n2.

I am trying to avoid an edge from n3 to n1, because I do not want n3 to influence the activation of n1; that way, if I complicate the graph, n1's connection to further nodes will not be influenced by n3. For example, if I introduce a fourth node (n4), and edge between n1 and n4 (e1,4), I do not want n3 to influence n1 to n4, only n1 to n2. The activation of n1 then acts via e1,2 to influence n2, and via e1,4 to influence n4. If n3 is then active, it will only influence the e1,2 edge, without affecting e1,4.

I am sure this is such a common problem that it has been addressed multiple times. I feel that I am phrasing my searches incorrectly due to lack of familiarity with graph theory.

jamie_2054
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    An edge connects two nodes. You cannot introduce a node with a single edge. The other end of that edge must connect to a node. Notice that this also precludes you from connecting an edge to an edge. It sounds like you may want weighted edges between your nodes where the weights are functions of some other properties. – John Douma Feb 20 '19 at 19:59
  • I mean, perhaps you’re thinking of multi-edges. – Zach Hunter Feb 20 '19 at 21:07
  • To me, this sounds more like a circuit ekement with three connections n1, n2 and n3, where n3 is a control input. There will be a fourth node inside the element. I wonder whether you'd be best modelling it that way (define the elements your network breaks down into, and see what ideas you can glean from introductions to circuit theory in electronic engineering) – timtfj Feb 21 '19 at 01:58
  • I think your building blocks need to be higher-level ones than nodes and edges. – timtfj Feb 21 '19 at 02:02

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