Create and plot two directed graphs, and then determine if they are isomorphic.

G1 = digraph([1 1 1 2 3 4],[2 3 4 4 4 1]);
G2 = digraph([3 3 3 2 1 4],[1 4 2 3 2 2]);
subplot(1,2,1)
plot(G1)
subplot(1,2,2)
plot(G2)

isisomorphic(G1,G2)

ans =

  logical

   1

Create and plot two graphs, G1 and G2.

G1 = graph([1 1 1 2 2 3 3 4 5 5 7 7],[2 4 5 3 6 4 7 8 6 8 6 8]);
plot(G1,'XData',[1 4 4 1 2 3 3 2],'YData',[4 4 1 1 3 3 2 2])

G2 = graph({'a' 'a' 'a' 'b' 'b' 'b' 'c' 'c' 'c' 'd' 'd' 'd'}, ...
    {'g' 'h' 'i' 'g' 'h' 'j' 'g' 'i' 'j' 'h' 'i' 'j'});
plot(G2,'XData',[1 2 2 2 1 2 1 1],'YData',[4 4 3 2 3 1 2 1])

Determine whether an isomorphism exists for G1 and G2. The result indicates that the graphs are structurally the same despite their different labels and layouts.

tf = isisomorphic(G1,G2)

tf =

  logical

   1

Use two different comparisons to determine if there is an isomorphism relation between two graphs. One of the comparisons preserves a node property, while the other ignores it.

Create two similar graphs. Add a node property Color to each of the graphs.

G1 = graph({'d' 'e' 'f'},{'e' 'f' 'd'});
G1.Nodes.Color = {'red' 'red' 'blue'}';

G2 = graph({'a' 'b' 'c'},{'b' 'c' 'a'});
G2.Nodes.Color = {'blue' 'blue' 'red'}';

Plot the graphs side-by-side in the same figure. Color the nodes red that have Color = 'red'.

subplot(1,2,1)
p1 = plot(G1);
highlight(p1,{'d' 'e'},'NodeColor','r')

subplot(1,2,2)
p2 = plot(G2);
highlight(p2,'c','NodeColor','r')

Determine if the graphs are isomorphic, ignoring the Color property.

tf = isisomorphic(G1,G2)

tf =

  logical

   1

Determine if the graphs are isomorphic and preserve the value of the Color property in the comparison. In this case, there is no isomorphism since the Color property of each graph contains different numbers of 'red' and 'blue' values.

tf = isisomorphic(G1,G2,'NodeVariables','Color')

tf =

  logical

   0