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Your friends will probably have more friends than you. Don’t worry, it’s nothing personal. It’s just a matter of how the networks are organized.
We can represent a friendship group as a network. Draw a node (dot) for each person and a line between the two nodes if the two people are friends. By doing this for a group of people who interact in person or online, we can create a representation of friendship.
This network allows us to explore questions such as the number of degrees of separation. If someone is a friend of your friend, they are connected to you at level 2. Their friends are at level 3, and so on.
How many links do we have to follow to get from one person to another? Connections tend to cluster. Think of a group of friends – the people you live with, some of your colleagues at work, or the people who attend your astrophotography club. Chances are, many of these people are friends with each other, so many of your “friends of friends” in the group are also your direct friends.
But there are also far-reaching connections. Your old friend who moved to another country has his own dense cluster of friends who all go to their soap carving club. All of these people are your 2nd degree relatives even if you have never met them.
Hence the famous claim of six degrees of separation. If you follow these more distant connections, you can quickly get beyond your own network. An old colleague who got a job in London goes wargaming with a barista working near Parliament, and suddenly you’re just steps away from shaking hands with the Prime Minister.
What about popular people? In a friendship network, some people will naturally have more connections than others. Imagine a group of 20 people, 15 of whom are friends with Sandy and five with Charlie. If we pick someone at random, there is a ¾ chance that they are friends with Sandy and only a ¼ chance that they are friends with Charlie. Your friends aren’t a random selection from your group: you’re more likely to be friends with more popular people, so you’ll find that your friends have more friends than you.
This phenomenon, called the friendship paradox, can be useful when sampling to find influential individuals. If you take a random sample from a group of people, you would expect them to have an average number of connections. But if you ask them to each randomly name a friend, chances are they’ll name someone who has more friends than they do. This new group will likely have an above-average number of connections.
So if your friends seem to go to more parties, your friends at work have more connections, and the friends in your art class seem to be in more clubs than you, don’t feel deprived—it’s the joke of network dynamics.
Peter Rowlett is a mathematics lecturer, podcaster and author based at Sheffield Hallam University in the UK. Follow him @peterrowlett
These articles are published weekly at
newscientist.com/maker
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