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760 pages!

I skimmed through the graph visualization section. It’s quite interesting.

Is there a version in print?
From the authors blog:

"A print-on-demand version will be available soon (link will follow)"

That page count and breadth of topics are repelling. Is there something original or exceptionally interesting in there?
It's an atlas, so no. It's supposed to be a broad cover you can skim and dig into some of the sections.

It's also not that huge given the scope -- it could be taught as a multi semester course like a lot of the similar statistics textbooks

>Is there something original or exceptionally interesting in there?

Presumably the exercises and organization, if nothing else, both of which end up being a large part of the value of any good textbook anyways.

Wow. This is a full-blown book, not merely a post or a paper. A thorough mathematical survey of network science (probability, graph theory, path analysis, etc.). Downloaded my copy. Although I wouldn't mind paying some money for the printed tome.
Print it yourself
That doesn't support the author though.
You have an option to become his patreon starting at $5/month
This is amazing.

I was lucky enough to study a bit of network science in college under a fantastic professor, and always regretted not taking it further and getting involved with his research.

It impacted my thinking in so many areas (finance, technology, etc.) and the only limiting factor was forgetting over time what I had learned. There's been hardly any good introductory resources for network science given what a young field it is. Great to see that changing!

What's the proper way to term the relationship between "Network Science" and "Graph Theory"?

Is it incorrect or too simplistic to say that network science is a subset of graph theory?

Network Science is an interdisciplinary field for the study of complex networks. Graph Theory is the mathematical study of graphs.
Would it be incorrect to say network science is the interdisciplinary study of an aspect from graph theory? Is there a complex network that isn't or can't be represented as a graph?
You could say that. Graph Theory is a method or theory used in Network Science. Graphs in the wholly abstract is not of interest to Network Science though.
Very cool quote from the book:

"One of the facts that never fails to blow my mind is the realization that a piece of software is, after all, just a very cleverly composed number. Thus you can sum Adobe Photoshop to Google Chrome, although the result won’t probably make much sense. That is also why there exist such a thing as an “illegal number” [1]."

[1] https://en.wikipedia.org/wiki/Illegal_number