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.