Shortest paths need the right cost
Select an edge-weight definition that matches the business meaning of a shortest-path question.
A shortest path is not automatically the easiest path. The graph gives you possible routes. The edge weights define what "short" means. Hop count answers reachability If every edge has equal cost, shortest path means fewest relationships. That is useful for simple reachability, dependency tracing, and first-pass exploration. Weighted paths answer effort If edges carry time, money, latency, friction, privilege, probability, or risk, shortest path means lowest total cost. This is usually closer to how operations, security, logistics, and customer teams make decisions. Direction changes the answer In directed graphs, A can reach B without B reaching A. That matters…
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