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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(n1)/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
walk
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 walk 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.
Here is an example of a undirected graph:
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 Fall '09

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