As recently announced at HPEC 2020 GraphBLAS BOF, NVIDIA is contributing CUDA support to the SuiteSparse GraphBLAS library for sparse matrices. It would be interesting to see how the TCU work from this paper could influence that contribution!
Sparse matrix multiplication of an adjacency matrix is the same operation as one step in a breadth first search across a graph. This is why sparse multiplication is so important to optimize.
Dense matrices with N^2 space requirements simply can't hold or work with very large graphs, where as sparse (order N) and hypersparse (<< order N) techniques in GraphBLAS mean much higher density graph networks can be stored.
A great video on the mathematical foundations on the graphblas can be seen here:
Any to plug my own work, here's an introductory video on using the GraphBLAS with python:
Is it under the same Apache license as SuiteSparse:GraphBLAS?
 Tensor cores is a poor name, likely from marketing, as the units really only compute fixed, small matrix sizes.
(I am the pygraphblas author)
It would be nice if people could share some experiences.
Dense matrices are great, and their implementation is straightforward, a dense chunk of memory contains every element in the matrix, for an N sided square matrix, the storage requirement is N squared. Finding an element is a simple matter of indexing math. For large adjacency matrices, this is horribly inefficient, and the bigger the graph gets the worse the cache and memory locality as most elements end up being zero.
Hypersparse graphs, like say a large social network, may only have a few hundred billion edges, but trying to fit that in a dense adjacency matrix means requiring quadrillions of mostly empty elements. This is clearly impossible, so sparse matrices are required to store a large graph.
The C++/CUDA backend to cuGraph contains many low-level graph operations on really sparse graph structures as well: https://github.com/rapidsai/cugraph
rust wrappers for GraphBLAS
Java wrappers for GraphBLAS
JNI bindings are only built for Linux, if you need MacOS or Win feel free to raise an issue.