Mercyhurst UniversityDept of Math and ITDr Williams Home

Complete Graphs

Graph Options


Appearance Options

Edge Color: #
Background Color: #
Node Size:
Edge Thickness:

Animation Options

Draw By: Nodes    Parallels

Graph Information

Total Edges:
Max Degree:
Min Degree:
Mean Degree:

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

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.