To better understand graphs, let's look at Facebook and how you typically use Facebook. Every day you use your smart phone to post messages on your friend's wall or update your status. Your friends are all posting messages and photos and videos of their own.
You have friends, your friends have friends, who have friends, and so on. Facebook has settings that let you make new friends or remove friends from your friend list. Facebook also has permissions, which allow granular control on who sees what and who can communicate with who.
Now, when you consider that there are a billion Facebook users, the friends and friend's friends list for all users gets quite large and complicated. It is hard to even comprehend and manage all the different relationships or friendships.
So, if someone wants to find out if you and another person X...