Dear Avi, Henry,
Diagrams are a mixed bag, a complex and polymorphic species, in Peircean semiotics. All diagrams in common use, especially in mathematics, involve all three types of signs — Symbols, Icons, Indices — as interpreted by their user communities. There has been a tendency in recent years to overemphasize the iconic aspects of Peirce’s logical graphs, reading them a bit too much on the analogy of venn diagrams, but their real conceptual and computational power comes rather from their generic symbolic character.
Here’s an intro to Sign Relations from a Peircean point of view, still a bit “working on it” from my POV.
Here’s the skinny on the three main types of signs — Symbols, Icons, Indices — in Peirce’s theory of signs.