Why is it that my friends on Facebook seem to have more friends than I do?
Ally Kenny, St Joseph's Presentation
Convent, Lucan, Dublin
Professor James Gleeson
Networks, and the maths needed to understand them, are all around us. The brain is a network of neurons; the internet, a network of computers and routers; the worldwide web, a network of webpages and hyperlinks.
Facebook and Twitter are the most obvious examples of web-based social networks in our lives
Networks are very important to our social structures and our health, but we are only beginning to understand some of their most basic properties. This involves combining the mathematical subject of graph theory with computer science, as well as ideas from physics, biology, sociology and economics.
If you count how many Facebook friends you have, and how many friends each of your friends has, it is quite likely that you will find that your friends seem to have (on average) more friends than you do.
This is called the "Friendship paradox" or the "Feld paradox", after the sociologist Scott Feld who described it in his 1991 paper.
The mathematical reason is actually quite simple to explain. Imagine the following two people on Facebook: James is very introverted and has few friends (he is probably a mathematician!), while Terry is very popular and already has many friends.
So who are you more likely to have a friendship link with? Because Terry has so many friendship links in the network, and James has so few, it is more probable that you are linked to Terry than to James.
In fact, the more popular people are, the more likely they are to be a friend of yours; it is relatively unlikely that you are connected to unpopular people.
The result is that the average Facebook user finds their friends have, on average, more friends than they do. You might think this is just saying that you are more likely to friend someone who is already very popular, but in fact it's deeper than that.
The Friendship paradox has important applications in choosing how to target immunisation or vaccination strategies for diseases that spread through contact networks which describe the group of people who are in close daily contact and so capable of spreading infection to each other.
If randomly chosen people are asked to list their friends and contacts, the mathematics of the network structure means the listed people are better targets for scarce resources, as they are likely to be better connected than average. In fact, researchers in Harvard did just this during the 2009 flu season and found that the listed friends showed flu symptoms sooner than the rest of the population, thus giving a means of predicting the flu epidemic before it impacts the population at large.
As part of her final-year project, UL mathematics student Rachel Harrison has been examining the Friendship Paradox on Facebook.
Her results indicate that over 80pc of Facebook users have fewer friends than the average of their friends' number of friends. So if your friends seem to have more Facebook friends than you do, you are certainly not alone.
Irish Independent Supplement