Robin Milner defined bigraphs as a type of graphical structure with graph-like structure but where the nodes can be nested. They generalise process calculi like CCS and the $\pi$-calculus, but Milner seems to have intended for them to be used much more generally: the seminar notes from shortly before his death detail recent developments.
Looking back instead of forward, the prologue of Milner's 2009 textbook The Space and Motion of Communicating Agents, does not provide much of a historical background. Milner explicitly acknowledged its roots in Mobile Ambients and the Pi calculus. Yet the model is so general that there are bound to be strong links to older models.
Are there historical predecessors of bigraphs?
Focusing on the syntactic elements rather than the way they are used to capture evolving systems, an obvious precedent is A. B. Kempe, A Memoir on the Theory of Mathematical Form, Philosophical Transactions of the Royal Society of London 177, 1–70, 1886. Kempe's paper may have introduced vertex and edge coloured graphs (I am ignorant of earlier usage but would welcome pointers). Kempe also appears to have had some of the same kinds of general applications in mind that Milner envisaged. Are there other predecessors that should be mentioned?
(Edit: now marking this a community wiki, in the hope of attracting further answers.)