## Main Concepts

Linear Algebra

Matrix Multiplication

## Duration

30 minutes in class

## Summary of Activity

The simple idea of this well-known game is to find link between two entries of the wikipedia encyclopedia by using the blue hyperlinks. It is said that no two pages are further than 6 hyperlinks away from each other. Students can play with a few examples, create their own challenges for others. We can answer a few questions related to matrices and powers of (gigantic!) matrices in the context of this game. Then, by connecting to the webpage  https://www.sixdegreesofwikipedia.com/, we can conclude by discovering the optimal paths for the challenges that the class started with and attempt to break the commonly accepted fact that “we never need more than 6 clicks”! (After all, to prove such a proposition, all we need is to exhibit one counter-example). The activity here invites students to reflect on the meaning of the powers of that matrix.

## Notes and Insights

As described on the webpage https://www.sixdegreesofwikipedia.com/, the game is inspired by the concept of six degrees of separation, which claims that no two people in the world are more than six steps away if we link them by friends of friends of friends…

The hyperlinks in wikipedia can be considered as an enormous matrix where every page is listed in a row and a column. If a certain page A has a hyperlink to another page B, then a 1 is written in the row of A and column of B. If no hyperlink exists, then a 0 appears in the matrix.