I wonder if data structure with these definitions already has some of it's properties investigated (maybe it even has a name?):

  • nodes have similar amount of edges
  • between any 2 nodes there is a maximum length path of the same length as between any 2 other nodes

Example with maximum path length = 2

The properties I'm critically interested in:

  • maximum length path calculation per amount of nodes and edges per node
  • algorithm to [programmatically] build such graph with arbitrary amount of nodes and edges per node

I'm not familiar with any areas of study concerning these graphs, although that doesn't mean they don't exist.

With this in mind, it would seem to me that it may be a better idea to investigate which of these types of graphs are possible. You've shown that a $(5,2,2)$, (5 nodes, 2 edges per node, max path of 2), type of this graph is possible, but what about $(7,2,3)$? (523,13,8)? I'd be willing to bet that the process of finding which of these graphs are possible will be enlightening as to how to design an algorithm to accomplish their construction.


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