Eulerian Circuit

I was doing a question, in which indirectly I was required to check Eulerian Circuit

Can u please check and tell, if the below method is correct to check Eulerian Circuit

To check eulerian ckt,
we do 2 things :

  1. We need to make sure that indegree and outdegree of node is same. [ must be true for all nodes ]

  2. We need to check if all the nodes are in single connected component, this can be done either by applying DFS from any node and checking if all nodes are visited by a single DFS call, or we can apply kosaraju to find number of stronly conn. comp.

in second step, I can use DFS bcz. I am sure that indegree and outdegree is same for a particular node [ true for all nodes ]