Ask HN: What are the top takeaways of graph theory?

Some domains have theories which can be readily applied to other domains fairly easily - their main theories and implications are highly abstractable and generalizable.

For example, in finance: efficient markets, compounding, risk, option theory (to name a few).

In statistics: a distribution, statistical significance, correlation, sample selection.

In biology: natural selection, genetic algorithms, gene expression.

Many of these theories, frameworks and models can be applied to other domains.

What are the top takeaways from graph theory? The most generalizable? (For example, centrality, optimal paths, complexity). I'd greatly appreciate any concise resources pointing me in the right direction.