The best way to find fellow travelers?

Question

PHP

What is the best way to find fellow travelers?
Let's say I'm going from A to B. But, along the way there is a fellow traveler F who goes to C, and the road to C passes through B - that's what I need.
What technologies (or API can) apply? I read about Dijkstra's algorithms, but somehow it doesn't seem to fit this task. Or fit? In general, in which direction to dig? I can't find a similar issue anywhere.

Answer 1

The usual search for the intersection of paths in a graph.

Answer 2

Just open Cormen and study the chapter on graphs. I think then you will understand a lot, including about which algorithm and why it is better to choose.