What is a Graph? | Graph Theory

What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each edge joins two vertices, so the lines in the diagram of a graph will go from one vertex to one other vertex. Thus, the edge set of a graph consists of two-element-subsets of the vertex set, because in a simple graph, each edge is entirely defined by the vertices it joins. Oh by the way, we're only talking about simple graphs, which are the most well-studied types of graphs in graph theory, and are usually just called graphs. Among other restrictions, simple graphs don't allow for loops, multi-edges, or directed edges. We talk more about these restrictions in the video.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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