pygraphblas is a python extension that bridges The GraphBLAS API with the Python programming language using the CFFI library to wrap the low level GraphBLAS API and provide high level Matrix and Vector Python types.
GraphBLAS is a sparse linear algebra API optimized for processing graphs encoded as sparse matrices and vectors. In addition to common real/integer matrix algebra operations, GraphBLAS supports up to 960 different Semiring algebra operations, that can be used as basic building blocks to implement a wide variety of graph algorithms. See Applications from Wikipedia for some specific examples.
pygraphblas leverages the expertise in the field of sparse matrix programming by The GraphBLAS Forum and uses the SuiteSparse:GraphBLAS API implementation. SuiteSparse:GraphBLAS is brought to us by the work of Dr. Tim Davis, professor in the Department of Computer Science and Engineering at Texas A&M University. News and information can provide you with a lot more background information, in addition to the references below.
Matrices can be used as powerful representations of graphs, as described in this mathmatical introduction to GraphBLAS by Dr. Jermey Kepner head and founder of MIT Lincoln Laboratory Supercomputing Center.
There are two useful matrix representations of graphs: Adjacency Matrices and Incidence Matrices. For this introduction we will focus on the adjacency type as they are simpler, but the same ideas apply to both, both are suported by GraphBLAS and pygraphblas, and it is easy to switch back and forth between them.