my problem with this is that these relationships cannot be adequately modeled as complete, nor even undirected graphs. A love K_3 has no conflict that is to be resolved, thats just a throuple, how is one to make a drama out of it? Same for a love K_4 or indeed any love K_n where n∈ℕ. We need more interesting graphs for romantic storytelling, more precisely, digraphs with lots of single directional edges that can over the course of the story be worked into a collection of disjoint complete digraphs where the K_1 is only permissible if it has a loop. Preferably the selfcentered inlaws.
That’s a good point. Perhaps an ordinary love triangle must also be presented as a directed graph, and thus all generalizations should be a directed graph which would be equivalent to the above shapes if the graph were undirected and complete.
The generalization of a love triangle for n people is a n - 1 dimensional love simplex.
Of course, more complicated shapes probably exist too
Love Klein bottle
my problem with this is that these relationships cannot be adequately modeled as complete, nor even undirected graphs. A love K_3 has no conflict that is to be resolved, thats just a throuple, how is one to make a drama out of it? Same for a love K_4 or indeed any love K_n where n∈ℕ. We need more interesting graphs for romantic storytelling, more precisely, digraphs with lots of single directional edges that can over the course of the story be worked into a collection of disjoint complete digraphs where the K_1 is only permissible if it has a loop. Preferably the selfcentered inlaws.
That’s a good point. Perhaps an ordinary love triangle must also be presented as a directed graph, and thus all generalizations should be a directed graph which would be equivalent to the above shapes if the graph were undirected and complete.