In the branch of mathematics called **Graph Theory,** a **graph** bears no
relation to the graphs that chart data, such as the progress of the stock
market or the growing population of the planet. Graph paper is not particularly useful for drawing the graphs of Graph Theory.
In Graph Theory, a **graph** is a collection of dots that may or may not be
connected to each other by lines. It doesn't matter how big the dots are,
how long the lines are, or whether the lines are straight, curved, or
squiggly. The "dots" don't even have to be round!

All that matters is which dots are connected by which lines.

Two dots can only be connected by one line. If two dots are connected by a
line, it's not "legal" to draw another line connecting them, even if that
line stretches far away from the first one.

If you look at a graph and your eyes want to zip all around it like a car
on a race course, or if you notice shapes and patterns inside other shapes
and patterns, then you are looking at the graph the way a graph theorist
does.

##
Here are some of the special words graph theorists use to describe
what they see when they are looking at graphs:

## See also . . .