What's a graph? The image below is a graph.
If you'd like the technical explanation, this well-cited paper is a good starting place: Graph Drawing by Force-directed Placement. One of the important things about working with graphs is getting your hands dirty. The JavaScript interface at https://www.small-wide-world.com/ lets you do that. When you visit the page you should get one of the saved graphs that are embedded in the webpage. You can click on a node and drag it around. You don't have to put your cursor right on the node, it will select the nearest node to where you click.
If you want a little help, click Animate and it will try to make the distance between nodes the same.
If you want to create your own graph from scratch, I recommend the following clicks:
Click Clear
Click Add node for each node you want.
Drag the nodes to where you want them to be.
Click
Connect nodes.Drag from the node you want to connect to the other node. A line will form between the two when they are connected.
Click
Move nodes. Now you can drag them around if you want.Click Animate to improve the shape a little bit. Repeat as many times as you want.
Click Save JSON to make a copy so that you can use it once I get the import function working.
If you want to continue working on a network you saved, paste the JSON data into the text area above Import and click Import.