A famous example from graph theory is called the Kevin Bacon game with actors as vertices and movies as edges.

Connect the following Actors in one network. Only use movies, no TV shows. You can only use a movie one time as an edge. This is the list of the best actor/actress nominees from the last three Academy Awards.

Joaquin Phoenix, Antonio Banderas, Leonardo DiCaprio, Adam Driver, Jonathan Pryce, Anthony Hopkins, Riza Ahmed, Chadwick Boseman, Gary Oldman, Steven Yeung, Javier Barden, Benedict Cumberbatch, Andrew Garfield, Will Smith, Denzel Washington, Renee Zellweger, Cynthia Ervin, Scarlett Johansson, Saoirse Ronan, Charlize Theron, Frances McDormand, Viola Davis, Andre Day, Vanessa Kirby, Carey Mulligan, Jessica Chastain, Olivia Coleman, Penelope Crus, Nicole Kidman, Kristen Stewart.

Use this to help you find connectionshttp://oracleofbacon.org/it is basically a graph theory solver for the IMDB.

Your graph should end up looking something like this :

You've Got Mail Tom Hanks Sleepless in Seattle George Burns Apollo 13 Meg Ryan In the Cut Six of a Kind Kevin Bacon You've Got Mail W.C. Fields Parker Posey Clockwatchers Lisa Kudrow