It definitely feels like graphs/topology should be helpful tools to work with data(Since graph-like structures are good representations of the real world), but we need to solve this efficiency issue before this can be possible.
Also to address the confusion on how category theory comes into it, category theory studies abstract structures where you have objects and relationships between these objects. A lot of algebraic topology(Which is the sort of topology relevant here) is built in the language of category theory(Either by neccesity or by convention).