Network Theory

John Baez

Network Theory

Scientists and engineers use diagrams of networks in many different ways. Together with many collaborators I am studying networks with the tools of modern mathematics, such as category theory. You can read blog articles, papers and a book about our research. I am collaborating with the Topos Institute to use the resulting math for scientific computation, such as quickly adaptable models of infectious disease.


Here are papers, theses, and a book:


Classical mechanics:

Electrical circuits:

Control theory:

Markov processes:

Reaction networks:

Petri nets:

Stock-flow diagrams:

Graphs and quantale-valued matrices:

The mathematics of networks - decorated cospans:

The mathematics of networks - structured cospans:

The mathematics of networks - props:

Blog articles

Here is the main series of blog articles:

You can navigate forwards and back through these using the blue arrows. By clicking the links that say "on Azimuth", you can see blog entries containing these articles. Those let you read comments about my articles—and also make comments or ask questions of your own!

Chemical reaction networks, Petri nets and Markov processes

This was the official end of the series of posts on stochastic Petri nets and chemical reaction networks. All this material was made into a book: But there is more to read: There's also a series of posts on this paper, which concerns coupled reactions and conservation laws:

Here's the series:

Electrical circuits

Starting in part 27 of the network theory series, I changed topics to electrical circuits and related engineering problems. My series of blog posts fizzled out after 5 more posts, since my students and I got busy writing papers. But here they are:

These ended rather prematurely when I decided to focus on writing papers instead. So, read some of the papers on circuits listed above — or at least these theses, which make a great overview:

To understand ecosystems, ultimately will be to understand networks. - B. C. Patten and M. Witkamp

Text © 2020 John Baez