**What is a graph?**A graph is simply a bunch of nodes (usually drawn as circles) connected by edges (usually drawn as lines). Here’s Wikipedia’s picture of a graph:

**Okay, so what are k-vertex-connected graphs**? In the graph above, if you remove node numbered 4, then the graph becomes

*disconnected*. Because you can remove just one node to disconnect the graph, the graph has a kappa of one. Here’s another example graph: The graph above has four nodes. You can remove three nodes and the graph still remains connected. Thus, the kappa constant for this graph is four.

**How does this have anything to do with education**? You can represent

*topics*a student learn as nodes, and you can represent topics that are related as having edges between them. Connections are made when students discover an application that involves two topics, or discovers a more complex phenomenon that requires the understanding of two topics. The

**more and better connections**you have between topics you learn,

**the higher the chance knowledge will stick and have a lasting impact on your life**. The fast your gain those connections, the more effectively your learning will be. Thus, Increases in kappa on an knowledge graph are key to effective and efficient learning. That’s why the kappa rate is important. Plus we liked how it sounded like apparate from harry potter. Who can say no to free and instant travel?