GraphBLAS

On the software side I can recommend https://github.com/DrTimothyAldenDavis/GraphBLAS It is hard to make a sparse linear algebra framework, but Tim Davis has been doing a great job collecting the various optimal algorithms I to a single framework that acts more like an algebra than a collection of kernels.

Yep, for any decent sized graph, sparse is an absolute necessity, since a dense matrix will grow with the square of the node size, sparse matrices and sparse matrix multiplication is complex and there are multiple kernel approaches depending on density and other factors. SuiteSparse [1] handles these cases, has a kernel JIT compiler for different scenarios and graph operations, and supports CUDA as well. Worth checking out if you're into algebraic graph theory. Using SuiteSparse and the standard GAP benchmarks, I've loaded graphs with 6 billion edges into 256GB of RAM, and can BFS that graph in under a second. [2] [1] https://github.com/DrTimothyAldenDavis/GraphBLAS [2] https://onesparse.com/

For a powerful sparse adjacently matrix C library check out SuiteSparse GraphBLAS, there are binding for Python, Julia and Postgres. https://github.com/DrTimothyAldenDavis/GraphBLAS