User blog comment:Wythagoras/Graphs/@comment-1605058-20140913123957/@comment-1605058-20140913194344

There are still multiple ways to do this for fused cycles, and for alone cycles too if there are some outcoming edges.

How about fused cycles of different lengths? I also believe that, in a way, fused cycles are dependent on the drawing of a graph. Consider the following two graphs: http://puu.sh/bxAsq/bcbcca7ea7.png For me, it's clear from the pictures that the left graph is pentagon fused to hexagon, sharing three edges, and the one on the right is two pentagons fused, sharing two edges. Now guess what - this is same graph drawn twice!

I'm not gonna address the issue of not mentioning what to do with multiple fused cycles.