My intuition tells me that there is always a unique, single shortest path between any two nodes in a Kautz di-graph. Is this true ? If yes, why? If not, why not ?
My intuition is based on the fact that Kautz graphs are best known optimal degree-diameter digraphs, that is, for a given degree (d>2) and diameter the Kautz graphs are the largest known graphs. So in this sense, one could argue that Kautz graphs do not "waste" shortest path connections.