What is the name of a directed weighted graph in which an arc can have one of 3 weights: +, -, and x (for, e.g., 'like', 'dislike', and 'acquainted, but indifferent')? Note that the latter is not equivalent to the case of no arc.
Are there any results available for such graphs? I presume that they can be used in voting systems, maybe recommender systems, but I could not find any references.
There are definitely results concerning signed graphs. I am not so sure about the option with indifferent, but I guess somebody has looked into it.