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  1. An Euler circuit in a graph G is a simple circuit containing every edge of G.
  2. Strongly connected means if there's a path from a to b whenever a and b are vertices in graph G, then there exists path from b to a as well.

When I think about it, I reason that if there's an Euler circuit, it would mean there's a path from a vertex to any other vertex. Almost like a cycle. So that would make the graph strongly connected.

I just want to make sure if my thinking is wrong in anyway? Because I was unable to find this written anywhere specifically.

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Firstly, we need to assume that there is no single isolated node. Because, we may have an Euler circuit, but it would not ever pass the isolated node.

Having the assumption, I think the argument can be made more clear by saying that, since all the edges are to be covered with an Euler circuit, then all the vertices should be passed at least once. Therefore, we can definitely find a path between any pair of nodes.

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  • $\begingroup$ I had no idea a single isolated vertex could also be an Euler circuit! Thanks for clearing that up. :) $\endgroup$ – momo Sep 4 '17 at 15:54
  • $\begingroup$ No worries... :) $\endgroup$ – Med Sep 4 '17 at 15:55

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