The friendship paradox and Social Network Analysis
The friendship paradox says that in most cases, on an average, your friends will have more number of friends than you have. This seemingly paradoxical aspect was first observed in 1991 by Scott L. Feld, who was a sociologist. This simple fact has since then been used to model networks in many studies.
In a network analysis perspective, it states that, in a friendship network, a node will have a degree which is less than the average degree of rest of the nodes. Though this cannot be considered as a mathematical certainty, but it turns out to be true in many real life networks. This has also been found to hold in many other fields, and is called as the Generalised Friendship Paradox (GFP). The GFP holds for a node if the node has some lower characteristic than the average characteristic of its neighbours¹. For example, it has been found that, generally, the co-authors of a paper will have more publications, citations etc., compared to the author himself. Mostly, there is a good chance that your twitter friends are better connected than you.
The preferential attachment process
An intuitive reason for the friendship paradox could be the preferential attachment process that drives many of the real world network formations. According this model, the probability of a node to get attached to another node is proportional to the degree of that node. So it is more probable that you tend to be friend with a person who is well connected than a person with fewer connections².
The Friendship Index
In order to capture some characteristics of the friendship paradox, researchers have put forward a metric called the Friendship Index (FI)³. It is the the ratio of the average degree of the neighbours of the node to its own degree. That is, it would be the ratio of average number of your friends’ friends to the number of your friends. An FI value which is closer to 1 would indicate that the person experiences the paradox less severely, while higher values indicate an extreme manifestation of the paradox.
Psychological Impact
What could be the effect of a very high value of Friendship Index? It can sometimes create significant impact on the way people perceive themselves. They may think that their friends are more popular, happier and even wealthier than they are. This can have a psychological impact. With the popularisation of social networking platforms, the problem is likely to get much worser as it is much easier to compare oneself to others in such online platforms. According to Eom et al.¹, “This might be the reason why active online social networking service users are not happy”.
So if you’re an active social network user and if you find yourself feeling unhappy and inferior thinking that your friends seem to be doing better than you, understand that it’s a play of the friendship paradox, and you are not alone and almost everybody else on the network is in a similar position.
