The product graph construction. The corresponding basis vector in the respective Laplacian kernel is shown below each graph. For legibility, the vertices of the product graph are denoted i,j, rather than (i,j). All three graphs are strongly connected. The basis vector for the Laplacian kernel of graph G was calculated in Figure 4B, while that for graph H follows directly from Equation 7. The basis vector for the Laplacian kernel of G×H is given by the Kronecker product formula in Equation 14, as described in the text.