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Graphs

A graph consists of vertices and edges. And vertices are connected to each other by edges. From this point of view, graphs can be identified with 1-dimensional CW-complexes . As topological objects, graphs don’t look illuminating. Graphs are, however, useful when we describe combinatorial data mathematically. As a generalization of knot theory , we can study embeddings of graphs topologically. Ribbon graphs are also important in low-dimensional topology.

There are many variations. We can color vertices or edges. We can also orient edges. Directed graphs are called quivers .