graph theory (thing)

A directed graph is one in which the edges are assigned directions, like one-way streets; that is, an edge may go from A to B but not from B to A. Directed graphs may have some bidirectional edges as well.

A graph is simple if there is only one edge between any two nodes. Otherwise the graph is nonsimple. A nonsimple graph may have some special edges called loops which go from one node back to the same node.

There are many other types of graphs with special names, but I will only describe one more here. A planar graph is one which can be drawn or embedded in a plane without any of the edges crossing, other than at nodes. For such graphs, Euler's formula holds, as is the case with convex polyhedra.

In much of the study of graph theory, only the nodes and the connections made by the edges matter, so the graph can be arbitrarily twisted and still remain the same graph; thus graph theory borders on topology.

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