GraphDB in PHP by Alessandro Nadalin and David Funaro.
Well, at 163 slides you know there is going to be some introductory graph material but it went by quickly enough. Would have liked to see the presentation that went with the slides but even without it, the slides are fairly interesting.
Good to see PHP libraries because PHP is so widely used as a scripting language. (No offense to others, just an observation. Use whatever is the most comfortable for you.)