A branch of discrete mathematics. The
study of relations, connections, networks, connectedness, and especially graphs. A graph is a pair of sets. The elements of the first
set are called vertices. They can represent
people,
words, letters, cities, brain cells, web pages, countries, or anything that can be associated with, or connected in some concrete or abstract way, to something else. The elements of the second
set are pairs of elements from the first
set. They are called edges. They can be unordered pairs or ordered pairs. In the latter
case, the edges are called directed edges, and the graph is called a digraph.
To picture a graph, think of dots connected by line segments to other dots. Each line segment must have a
dot at both ends. Neither the shape nor the length of a line segment matters in graph theory. All that matters is which dots are connected to which dots. You can give them names, numbers, letters, and/or colors. Or you can color the edges.
Graph theory can
help you to understand games, hierarchies, networks, family trees, food webs,
flow charts, algorithms, trains of thought, just about
anything you can think of!
