Transfer portals only match pairs: you need someone where you want to go who wants to come where you are. Most people never find them.
Loop finds the three- and four-way chains that pairs miss — then gets everyone to agree at once, before anyone's posting changes.
A graph engine searches every 2-, 3- and 4-way chain in your cadre and picks the set that moves the most people.
Every seat in a loop is reserved together. One "no" releases everyone; silence expires on a deadline.
Partners see "Teacher · Nagpur", never names — until every person has accepted.