The article isn't about graphs-as-in-charts, but graphs as in the mathematical concept. In this case, expressing dependencies between different pieces of operational infrastructure, such that changes to one piece of infrastructure trigger automatic changes to other pieces.

Unfortunately, the author is pretty vague about exactly what pieces of infrastructure they imagine defining relationships between, and what triggers they might use. On the smaller side, they mention 'I changed a config, I must restart nginx' (micro level dependency between nginx and its config) and 'something changed in my app tier, need to tell my load balancer' (macro-level dependency between a service and its front-end). What kind of dependencies would be useful to define between services in a service oriented architecture, which are usually designed so as to minimize dependencies?