The graph is most definitely directed. One small example is Facebook -> Narcissism (1 path of 1 degree)[1] compared to Narcissism -> Facebook (8 paths of 2 degrees)[2].
[1] https://www.sixdegreesofwikipedia.com/?source=Facebook&targe... [2] https://www.sixdegreesofwikipedia.com/?source=Narcissism&tar...