This brings back memories of a similar port of Graphviz to the web I started (then unfortunately abandoned) years ago; it's likely this is way more optimized, but perhaps my project can serve as illustrative of what's needed for an Emscripten port: https://github.com/bpartridge/graphviz.js

EDIT: or rather, what was needed for such a port a few years ago; I think it's been made much simpler since then!