Do either of Paul Erdős or Kevin Bacon have a Ryu number? Does Ryu have an Erdős or Bacon number?
From the top: Paul Erdős, for all of his prolific mathematical contributions, doesn't appear to be in any video games. Granted, it's not like there's great documentation for mathematicians that are in video games. The only method I could find easily is through Great Scientists and Engineers in Civilization games, and Erdős doesn't crack that list. Thus, Paul Erdős does not have a Ryu Number.
As for Kevin Bacon, Topher Florence in a 2019 Fanbyte article gave Kevin Bacon a Ryu Number of 6 (UPDATE: now 5 with Ryu’s inclusion in Brawlhalla) (UPDATE 2: 4, courtesy of @kchasm) through Bacon's sole video game credit as a celebrity guest appearance in You Don't Know Jack Vol. 2.
There are three caveats that I've discovered while doing additional research, however.
First, the path goes through the trivia game TV Land Presents: Blast from the Past, a video game that definitely exists but has virtually no documentation outside of a cast list, so it's a somewhat small leap of faith to use it.
Second, Florence mentions that American radio announcer Gary Owens is the narrator for Space Quest IV: Roger Wilco and the Time Rippers and refers to himself, out loud, as Gary Owens. Both of which are true... just not at the same time. Owens was the narrator for Space Quest IV, but at least as far as online transcripts and the Space Quest Omnipedia can attest to, the narrator only explicitly refers to himself as Gary Owens in Space Quest 6: Roger Wilco in the Spinal Frontier. So does this mean that the narrator voiced by Gary Owens in Space Quest IV is also explicitly Gary Owens? I mean, most likely, but also unless there's a line that implies the narrator in 6 is or is not the same narrator in IV, it's not 100%?
Third, the link from Owens to King Graham is through a brief cameo in Space Quest IV of someone getting carried away by an eagle in direct reference to King's Quest V: Absence Makes the Heart Go Yonder!. The sprites are nearly but not quite identical, but what complicates matters is that apparently in the game files that person is identified as Maharg. So on one hand, the sprite is just about identical, but the person in Space Quest IV is named something different, but it's also just as likely that it was a cheeky touch by a Sierra dev and not meant to signify a different character?
The first caveat has to be accepted to give Bacon a Ryu Number (and in all likelihood, it's probably fair game). The second and third caveats, however, can be bypassed, but it gives Kevin Bacon a tenuous and possibly unprecedented Ryu Number of 7 (UPDATE: now 6, see above update), barring an alternate route I overlooked.
(CORRECTION: Per @froglord999, nevermind all of that.)
As for Ryu's separation numbers, it is extremely difficult for a fictional character to have a movie credit (but not unheard of) and near impossible for a fictional character to coauthor a research paper, so Ryu does not have a Bacon or Erdős Number.
But just for the hell of it:
Ryu's single theatrical movie depiction is in 1994's Street Fighter portrayed by Byron Mann, who per the Oracle of Bacon has a Bacon Number of 2.
Likewise, Mike Moh, the actor for Ryu in Street Fighter: Assassin's Fist, a live action web series officially approved by Capcom, also has a Bacon Number of 2.
An associate professor in the Department of Computer Science at George Mason University named Yotam Gingold has an Erdős number of 3, and happens to have published a 2006 paper titled "From Rock, Paper, Scissors to Street Fighter II: Proof by Construction". And guess who’s in Figure 4?
