About Complete Graphs
In a complete graph, every node is connected by an (undirected) edge to every other node. Every node will have the same degree; if there are \(n\) nodes, then each node is connected to the remaining \(n-1\) nodes, so the degree of each node is \(n-1\). The number of edges is also easy to calculate: \(n(n-1)/2\).
Using the Applet
There is only one parameter for this graph, the number of nodes \(n\). You can adjust the appearance of the graph using the options provided (colors should be entered as hex values, without a hash symbol). To watch the graph being drawn, check the Animate box and select the speed of the rendering. For the complete graph, you can watch the graph being constructed in two ways: by drawing all edges out from each node, one at a time, or by drawing parallel line segments (this is a slightly easier approach when drawing these graphs by hand).
Hovering over a node will highlight the edges it is connected to, and display the nodes to which it is connected.
About this Applet