They're really compelling but oddly unpopular.
Imo, they're useful for one-off pattern discovery, and they're most valuable for finding single or a few exceptions and outliers in normalized data, and you need to be in an environment where there are asymmetric returns on finding those. Surveillance seems to be their default use case, with open ended scientific research a close second. This comes up with graph based recommendation engines, which are essentially a surveillance/marketing product based on preferences. Most businesses aren't based on discovery of anything other than customers for a transaction they already have.
These aren't problems engineers typically solve, which are more about scaling and optimizing, they're more marketing and sales problems, where you're looking for exceptions and opportunities. (security and privacy are the complementary antithesis of these) A graph based product (imo) is ideal for product marketing analysts optimizing for customer preferences and discovery.
From a product perspective, graphs are analogous to ML, where you'd use a clustering algorithm on loosely structured data to yield categories, comparisons, and implied relationships, whereas a graph yields the same thing over the structured normalized data you can feed into it once you have imagined an ontology to fit it.