I think it's a question of improbability: the impressiveness of any result is directly related to its unlikelihood of appearing on the assumption that graph edges appear at random with an appropriate probability distribution.
Self-links are known to be common (eponymous albums and/or songs). Hence the base probability model on which to judge impressiveness should reflect that, by considering self-links to appear with a significantly larger probability than non-self links. So including a self-link in a cycle doesn't increase its impressiveness by very much (so I'd be inclined to consider it a cheap trick), and finding a cycle entirely composed of one self-link is definitely too easy to be a challenge. But two nontrivial cycles sharing a vertex would be a more impressive find, so I'd accept the resulting figure-8 as a worthwhile result.
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Self-links are known to be common (eponymous albums and/or songs). Hence the base probability model on which to judge impressiveness should reflect that, by considering self-links to appear with a significantly larger probability than non-self links. So including a self-link in a cycle doesn't increase its impressiveness by very much (so I'd be inclined to consider it a cheap trick), and finding a cycle entirely composed of one self-link is definitely too easy to be a challenge. But two nontrivial cycles sharing a vertex would be a more impressive find, so I'd accept the resulting figure-8 as a worthwhile result.