*Theorem*
A

graph is Eulerian (i.e. a Euler tour is possible)

if and only if all its

vertices have even

degree. That is at each point, the number of edges going into that point is even.

If a graph has 1 or 2 vertices of odd degree then it is Semi-Eulerian, that is a tour covering each edge is possible but it won't start and finish at the same node.