No, it's not nonsense at all. GraphBLAS does rely on semirings on sparse matrices, so it does use linear matrix algebra. But it doesn't use or compute a kerne

No, it's not nonsense at all. GraphBLAS does rely on semirings on sparse matrices, so it does use linear matrix algebra. But it doesn't use or compute a kernel explicitly. A kernel is a vector x so that Ax = 0. There are places where y<m> = Ax = 0 is useful to compute (m is a mask, like a bulk-if statement, where y(i) is modified only if m(i)=1). If x is a set of nodes then A'x is the set union of the neighbors of x (assuming A(i,j) is the edge (i,j), which is typical but not required). Then if x has no neighbors in the set m, then y = 0. I use this in the GraphBLAS implementation of Luby's independent set algorithm (in my Demo/ folder of SuiteSparse/GraphBLAS). There are lots of connections between linear algebra and graph theory. In this case, the idea of a kernel does find its place in a graph algorithm, but it's a special case. It's not something that appears everywhere in every graph algorithm.