Is there a much easier way to find the vertices of a Eulerian Path? If I have a $K_8$ graph like the one here
and I want to label the Eulerian path for the vertices? what would be the best way to do this, there has to be a better way then just going through the lines one at a time. I keep getting lost every time... how do mathmaticians approach this?
 A: Euler path finding algorithm:
STEP $1$: Locate the two vertices of odd degree. Pick one of them at random.
STEP $2$: Start walking from the chosen vertex. Make sure you don’t use the same edge
twice. Continue until you get stuck - this can only happen when you visit the other
odd-degree vertex and have used up every edge through it.
STEP $3$: Remove from $G$ all the edges you’ve walked along and let $G′$ be the remaining
subgraph. For each connected component of $G′$
, perform the Euler cycle finding algorithm.
STEP $4$: Glue together the hierarchy of walks so as to obtain an Euler path between the
two odd-degree vertices in the original graph $G$.

Euler cycle finding algorithm:
STEP $1$: Choose a starting vertex $v$ at random.
STEP $2$: Start walking from $v$. Make sure you don’t use the same edge twice. Continue
until you return to $v$ and have used up every edge through it.
STEP $3$: Remove from $G$ all the edges you’ve walked along and let $G′$ be the remaining
subgraph. For each connected component of $G′$
, go to Step $1$.
STEP $4$: Finally, when there are no edges left, glue together the hierarchy of walks so
as to obtain an Euler cycle in the original graph $G$.
