I think this statement is true because if node a can reach every node (including node b) and node b can reach every node (including node a), there is an edge between node a and node b. This means that every nodes other than a and b can connect with each others via the node a and node b edge. But I am not sure about how to formalize the proof.
2026-05-16 17:07:26.1778951246
In a directed graph with n≥2 nodes, if two different nodes reaches every nodes (including itself), then this graph is strongly connected.
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Here is a simple counterexample: