lec0302 - Undirected Graphs Graphs are composed of two...

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Undirected Graphs Graphs are composed of two components: vertices and edges. Vertices are essentially points. (They are also referred to as nodes.) Typically, they will be labeled on a graph. In an undirected graph, edges are simply lines in between pairs of vertices. So, for example, in a graph with n vertices, the maximum number of edges is n C 2 = n(n-1)/2. This is the number of edges in a complete graph. A complete graph is a graph where there exists an edge between all pairs of vertices. We will define the degree of each vertex of a graph to be the number of edges that are incident to that vertex. A path in a graph is a sequence of edges that can be traversed one by one. (This essentially means that the endpoint of an edge in a path has to be the starting point of the next edge in the path.) It is permissible for a path to start and end in the same place. (Or, of course, start and end in different places.) A graph is connected if there exists a path in between all pairs of vertices.
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