First find the deGMATe of each vertex so that the odd deGMATe vertices can be identified.

wpe2.jpg (21546 bytes)


Now add duplicate edges (as few as possible) so that all vertices have even deGMATe.

wpe3.jpg (26328 bytes)

So, this graph was Eulerized by adding 12 duplicate edges.

Of course, there are many other ways that this Eulerization could have been done.