Cygnus flies down the Milky Way with Deneb at its tail, but the constellation's most consequential modern discovery lies elsewhere in its body, in an object that helped convince astronomers that black holes were real rather than a mathematical curiosity.
Cygnus X-1, one of the strongest X-ray sources in the sky, was identified in the 1960s and through the following decade became the first object widely accepted by astronomers as a genuine black hole, a collapsed star so dense that not even light can escape its gravity, detected here only indirectly, through the X-rays given off by gas pulled from a visible companion star as it spirals inward. The case was strong enough, and contested enough while the evidence was still being gathered, that physicists Stephen Hawking and Kip Thorne made a wager over whether it truly was one, Hawking betting against, in what he later called an insurance policy against having worked for years on black hole theory only to see the things turn out not to exist; he conceded the bet in 1990 once the evidence had become decisive.
None of this involves the swan at all, since a black hole and the visible star feeding it are simply passengers riding along inside a constellation shaped, to the naked eye, like a bird in flight.
The dark rifts of dust visible against the Milky Way running through Cygnus, mentioned in the constellation's own article, are made of ordinary interstellar matter; Cygnus X-1 is something else again, invisible even in principle to direct sight.