With graph databases you can easily and efficiently model any kind of network, including ones that are hierarchical or almost hierarchical by allowing a node to refer to multiple parent nodes instead of one.
My original idea with my bookmark extension Spellbook was this latter kind of graph, and I implemented a prototype called Grimoire using Ruby on Rails and Neo4j graph database that worked very well.
The Spellbook currently only allows adding new bookmarks into the hierarchical structure imposed by browser APIs, but features an easy to use search feature to find the right category. Spellbook is available for Chrome and Firefox, but the Firefox version seems broken again by their API changes: https://github.com/peterhil/spellbook