2.8.3 Isomorphism Video
PROFESSOR: We've briefly looked at graph isomorphism in the context of digraphs. And it comes up in even more fundamental way really for simple graphs where the definition is a bit simpler. So let's just look at this graph abstraction idea and how isomorphism connects with it. This is an example of two different ways of drawing the same graph. That is here's a 257, and there's 257. It's connected directly to 122, as here. And also 257 is connected to 99, as here. And if you check, it's exactly the same six vertices and exactly the same eight edges. But they're just drawn differently. So we don't want to confuse a drawing of a graph, like these two, with the graph itself. The graph itself consists of just the set of nodes and the set of edges. And if you extracted that from these two diagrams, you would get the same set of nodes and the same set of edges. So same graph, different layouts. But here's a case where it's really the same ...