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Graph Products

In general, a graph product of two graphs and is a graph with vertex set and edges given by a function of the edges of and (the edge from to is denoted by ). The four most canonical such products are:
Cartesian: ,
categorical: ,
strong: ,
lexicographic: .
Except for the lexicographic, they are all commutative. It is natural to display such graphs on a grid; however, this can obscure adjacency by overlapping edges. Three options reveal the graph structure: perturb the vertex positions with random noise, use the sliders to specify a function distorting the grid coordinates, or curve the edges.
Alternatively, you can view the operation as an equation. For the Cartesian product, there is a special, additional embedding (and edge coloring) designed to highlight the subgraphs corresponding to the factors, and an angle parameter so you can adjust their relative orientation (the vertices can also be perturbed). Mousing over the vertices of any graph product in the equation view reveals the projections of the selected vertex.

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