Network message passing game

This game demonstrates ideas about closeness and betweenness centrality. It's related also to small world networks, and the famous six degrees of separation hypothesis, popularized through sociologist Stanley Milgram.

Rules of the game:

Everyone take a letter (A, B, C, ...). Each person select 1-3 class members they connect to, at random. These will remain fixed throughout one round of the game. Define a "maximum hops" value (suggestion: double the number of people in the class).

Definition: To stamp a message is to add your letter to the end of the stamping sequence.

Procedure: On a slip of paper, everyone writes the name of someone in the class they're not directly connected to, adds an optional note, and stamps it (the first stamp in the stamp sequence). Then pass it to someone you do connect to.

When you receive a note, check who it's for. If for you, take it, stamp it, and stop its circulation.

If it's not for you, stamp it; then if the number of stamps in the stamp sequence exceeds the max hops (you can set this at 20 initially), write X on it (fail), and stop its circulation. Otherwise (if the number of stamps does not exceed the maximum hops value), pass it to anyone you connect to.

The round ends when all messages are stopped.

When everything has stopped, tally the number of messages that reached their destination. What percentage reached the destination? Check their routes by examining the stamp sequence of each. Which person appears on the most paths? These are the statistics for this round.

Play the whole game again from the start, keeping track of the statistics computed at each round.

Reconstruct the network on the whiteboard and try to identify who is most central from the network.

Try the same with "random" routing of one neighbor (every time you pass a message, pick anyone at random to give it to). What happens in this case?