Eulerian Circuit

I was doing a question, which indirectly says to check if there is eulerian circuit

Can u please look at the below statements and confirm if it is the correct method of checking :::

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 ]