FRIENDSHIP PARADOX
Why are your friends more popular
than you?
DO YOU ever feel like your friends
are more popular than you are? That may be because it is true—for nearly
everyone. This odd result, dubbed the "friendship paradox", has most recently
seen in twitter. When researchers from the University of Southern California
looked at 5.8m micro bloggers (and 194m links between them) they found that, on
average, both the people a user follows and, worse, those who follow him, have
more followers than he does. How can this be?
The
friendship paradox was first identified in 1991 by Scott Feld, a sociologist
working at the State University of New York at Stony Brook. Back then, of
course, Dr Feld was looking at real-world social networks rather than online
ones. Then, last year, scientists from Cornell University confirmed that the
result holds for Facebook's active users (721m people at the time of the
research, joined by 69 billion virtual bonds of friendship). In fact, it
obtains for any network where some members are more popular than others. And it
stems from basic arithmetic.
Consider a
simple social network composed of four people: Prakash, Pavan, Ashok and Shashi.
Prakash's only friend is Pavan. Pavan is also friends with both Ashok and Shashi,
who are friends with each other, but not with Prakash. This means that Prakash
has one friend (Pavan); Ashok and Shashi each have two friends (one another and
Pavan); and Pavan has three. On average, then, each person in the network has
two friends (eight friends divided by four people). But now consider how many
friends each person's friends have (in other words, friends of friends). Prakash
has one friend, Pavan, who in turn has three friends. Ashok's friends are Pavan,
who has three friends, and Shashi, who has two, which means that Ashok's
friends have five friends between them (even though their lists of friends
overlap). The situation is analogous for Shashi. Pavan's friends, Prakash, Ashok
and Shashi, have five friends in all. So the total number of friends of friends
is 18. But the total number of friends in the network is eight, as before. So
the average number of friends of friends (ie, how many friends each person's
friends have) is 2.25 friends each (18 divided by eight), more than the two
friends, on average, of the four people in the network. The reason, of course,
is that Pavan, who has most friends in the first place, is also counted most
often in the friends-of-friends category, raising the average. The same is true
for other networks: a few well-connected individuals have more friends than
most people, and they skew the average for everyone in whose network they
appear (which, because of their connectedness, is a lot of people).
This number-crunching has some
intriguing consequences—other than to justify not getting worked up about your
relative social status. During the H1N1 flu outbreak in 2009, for instance,
Nicholas Christakis of Harvard University and James Fowler of the University of
California, San Diego, kept tabs on a large group of randomly picked Harvard
undergraduates. They also monitored the people those participants named as
friends. Remarkably, the friends became ill about two weeks before the random
undergraduates, probably because they were, on average, better connected. With
the world only imperfectly prepared for pandomic, being able to spot trends in
this way could be useful.
Reference :
Economist
 |
| Writer : Abhishek Vadlakonda PGDM Student at IFIM B School |
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