Examples of Graphs
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Graph Theory. David Easley and Jon Kleinberg. January 24, 2007. A graph is simply a way of encoding the pairwise relationships among a set of objects: …
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Networks: Spring 2007 Graph Theory
David Easley and Jon Kleinberg January 24, 2007
A graph is simply a way of encoding the pairwise relationships among a set of objects:
we will refer to the objects as nodes, with edges connecting certain pairs of them.
Edges in a graph indicate a symmetric relationship between their endpoints. Often we
want to encode asymmetric relationships, and for this we use the closely related notion of
a directed graph. A directed graph has nodes as before, but now each edge has a direction:
it goes from a node u (its tail) to a node v (its head). When we want to emphasize that
the graph we are considering is not directed, we will call it an undirected graph; by default,
however, the term “graph” will mean an undirected graph.
Examples of Graphs
Graphs are very simple to define: we just take a collection of things, and join some of them by
edges. But at this level of abstraction, it’s hard to appreciate the typical kinds of situations
in which they arise. In the first lecture, we saw a number of examples of graphs; here we
summarize again some basic contexts in…
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