Azara Blog: Microsoft analysis linkages between people using instant messaging

Blog home page | Blog archive

Google   Bookmark and Share

Date published: 2008/08/03

The BBC says:

A US study of instant messaging suggests the theory that it takes only six steps to link everyone may be right - though seven seems more accurate.

Microsoft researchers studied the addresses of 30bn instant messages sent during a single month in 2006.

Any two people on average are linked by seven or fewer acquaintances, they say.
The database used by Mr Horvitz and his colleague Jure Leskovec covered all of the Microsoft Messenger instant-messaging network, or roughly half of the world's instant-messaging traffic, in June 2006.

For the purposes of the study, two people were considered to be acquaintances if they had sent one another an instant message.

Examining the minimum chain lengths it would take to connect all the users in the database, they found the average length was 6.6 steps and that 78% of the pairs could be connected in seven links or fewer.

The number of steps of "separation" is bound to be not that high a number. Say that each person's friends has on average 25 friends who are not the first person's friends, so that each step out you are getting an (approximate) increase in the number of people covered by 25. (This is not quite true for various reasons.) Well, 25 to the power 7 is around 6 billion, which is the population of the planet, so that means 7 steps. If the 25 were instead only 5 then it would still take only 14 steps. That is the power of the exponential.

And of course the Microsoft sample is seriously biased because it consists of (relatively) rich people (compared with the world average), who not only have a geographic bias but who also might have more connectivity.

Still, it was a cute enough computer science exercise.

All material not included from other sources is copyright For further information or questions email: info [at] cambridge2000 [dot] com (replace "[at]" with "@" and "[dot]" with ".").