I have the following graph / path problem:

There is exactly 1 start node and 1 end node.

There are also X (in this case 7) nodes, each connected to all other nodes and the start and end node with different lengths of the paths. The visitor has to visit each and every node exactly once, starting at the start node and ending its path at the end node. Diagram

There may be Y (in this case 5) visitors (or path variations).

Assuming that all Y (or 5 visitors/path-variations) start at t0 at the start node (t1, t2, etc. representing the steps to the next node, independent from the path length). At t1, all of the Y visitors have moved to one of the X nodes, but each node is only capable of holding exactly one visitor for each step (t). There may not be more than one visitor at each step at the same node (except the start and end node obviously). Each path has tx steps.

I am now looking for a solution to get the most shortest but also most similar path lengths for all visitors/path variations Y through all X nodes in tx steps.

How can I solve this and is it possible to do that in Excel, Python or R?



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