Please allow me to use this example/metaphor to describe an algorithm I need.

Objects

• There are 5 thousand pennies.

• There are 50 cups.

• There is a tracking history (Passport "stamp" etc) that is associated with each penny as it moves between cups.

Definition

I'll define a "highly diffused" penny as one that passes through many cups.

A "poorly diffused" penny is one that either passes back and forth between 2 cups

Question

How can I objectively measure the diffusion of a penny as:

1. The number of moves the penny has gone through
2. The number of cups the penny has been in
3. A unit of time (day, week, month)

Why am I doing this? I want to detect if a cup is hoarding pennies.

Resistance from bad actors

Since hoarding is bad, the "bad cup" may simply solicit a partner and simply move pennies between each other. This will reduce the amount of time a coin isn't in transit, and would skew hoarding detection.

A solution might be to detect if a cup (or set of cups) are common "partners" with each other, though I'm not sure how to think though this problem.

Broad applicability

Any assistance would be helpful, since I would think that this algorithm is common to

• Economics
• The study of migration patterns of animals, citizens of a country
• Other natural occurring phenomena

... and probably exists as a term or concept I'm unfamiliar with.