Unless noted elsewhere, "graph" refers to the same thing as "diagram," which means the classic box-and-edge diagrams.

Boxes! Arrows!
I don't think that those of us in the world of math and computer science realize that "graph" means something very different to most people. To them, this is a graph:

A graph
I'll mostly use the word "diagram," though I'll likely slip into my native tongue and say "graph." That means the node-and-edge kind of graph.