Spectral Graph Theory

This is an interesting line in the development of topology, linear algebra and probability that may only be really well known in Serbia. It is mostly the result of the work of one man. See Dragos M. Cvetković: A brilliant scientific career that is going on.

The fact that the development of graph theory always has got its stimulus by the necessities of classical sciences (physics, chemistry) and, on the other hand was strongly speeded up through the development of computer science and modern technologies, can be perceived and realized by following the interests and engagements of Professor Cvetković and contents of mentioned monographs. In a significant part of his career he was interested, among others, in applications to chemistry, which was also naturally induced by his long and close collaboration with academician Professor Ivan Gutman, an eminent scientist, both a chemist and a mathematician, who has given an immense contribution to connections between graph theory and chemistry. Papers in this field in which Cvetković was author or coauthor were also reviewed in ”Chemical Reviews”. In later years Professor Cvetković moved his focus to applications to computer science and also published a considerable number of papers and some books of collected articles. ...

In a period of his full scientific maturity Cvetković initiated and organized the work on an interactive programming system, called "Graph", intended for researchers in graph theory, and was intensely dedicated to the realization of that project. In fact, "Graph" had many characteristics of an expert system, facilitated the work of many people and justified its creating. Nowadays, we have its improved successor – "Newgraph".

I learned about this from comments by ἑλλέβορος on my Weather Report 7/19/22:

... and the day before:

Which shows how useful it can be to do mathematics this way.

Here's ἑλλέβορος's comment:

I like Sabine Hossenfelder. Seeing the words stochastic lambda calculus caused my brain to kick into another mode. This is a paper I'm looking at http://elib.mi.sanu.ac.rs/files/journals/publ/73/n067p004.pdf I think it is generally in the direction of things I'm thinking about. Kinda impenetrably mired in the whole formalism of the thing. It is indeed hard to say something sometimes.

Here's my reply:

The abstract, which is all I've read so far, is exactly what I was thinking when you said product of graphs, but then what led to my musing about boolean networks was thinking that there are several different natural-sounding ways you could define the edges in the product graph. You could say, for example, that any vertex pair X=(a,b) in the product has an edge to Y=(c,d) if and only if a has an edge to c AND b has an edge to d, which is a kind of intersection product. But you could also define the product as a union product by saying (a,b) is connected to (c,d) iff either a is connected to c OR b is connected to d. Then you could also define a complement product which connects (a,b) is connected to (c,d) iff NEITHER a is connected to c NOR b is connected to d.  And then this looks something like a complemented boolean lattice. I will shut up now until I've read a bit more of the paper! 😂