OSPF Shortest Path First

How each router turns its area's database into one cheapest path to everywhere

Root: finalcandidatenot reached tree edgeruled out

Different trees, no loops

Every router builds a different tree from the same database, and they never send a packet round in a circle.

Each hop gets strictly closer. A's path to F costs 20 and its first hop, B, is 5 away, so B's own path to F costs exactly 15.
The cost still to go only shrinks, so no router can see the same packet twice.
A loop needs different databases. Just after a link fails, a router that has heard can send traffic back to one that has not: a short-lived micro-loop, closed when the news arrives.

The full explanation, with an example ↗

Candidate list

Shortest paths