Ever seen mathematical theory play out in real life? This is transitivity in its purest form. If person A shakes hands with person B, and person B shakes hands with person C, then by the transitive property, person A has technically shaken hands with person C. The Queen's reaction in the bottom right says it all – she just realized she's mathematically connected to every dictator on the planet through the Six Degrees of Diplomatic Handshakes. Next time your professor drones on about abstract mathematical relations, remember they're secretly describing how diseases and political scandals spread through fancy receptions.