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Physicists and sociology

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Physicists and sociology

A story of networks and sociopaths

Physicists are known to be socially awkward [reference needed]. Despite this sadly poorly documented [1], widely believed and easily caricatured by sitcom of debatable quality fact, a current trend is to ask them to use their expertise to study human social organizations, such as networks of friendships.

Isn’t social ineptitude a disadvantage when it comes to such subject? All the opposite dear, it is of great help! Here is a well known discussion, reported in Ref. [2], between Albert-László Barabási, a renowned physicist of the field, and an anonymous sociologist that perfectly exemplify why it is the case:

“I have an idea! We could approximate people by point-like dots!

– Wait a minute, Albert-László, I don’t think it…

– And friendship could be a solid line! A nice, straight, infinitely fine solid line!

– Friendship? The complex immaterial bound between two…

– Exactly! It will be much simpler to study.

– …

– Isn’t it great?

– Listen. I don’t know how to tell you that, but… no sane person will ever consider that a good representation of people or of friendship.

– That’s why it’s smart! That’s why you needed a physicist all along!” [3]

The point here is simple: if you are profoundly ignorant of what social interactions are, you are in a good mental state to be able to represent them in a simple, objective and inanimate fashion [4]. The representation favored by physicists is the network, an ensemble of nodes (also known as vertices) connected by edges. Importantly, nodes are fully determined by which other nodes are connected to them. They have no family, no gender, no god, no master, no past, no hope, no future [5]. The only thing that matter is who are their friends. Seeing that their friends have more friends than themselves makes them miserable? It’s irrelevant!

Wait a minute… no it is not. Well, their sadness obviously is irrelevant [6], they are only point-like dots after all. The fact that they see their friends having more friends than themselves, however, is not. Are this sad dots simply unlucky, or is there something deeper in the structure of the network which can explain why they feel so miserable?

As it turns out, there is. If we have n dots in our friendship network and we not kj the number of friends of dot j [7], then the average number of friends F0 is

Counting the friends of friends is a bit more tricky, the key point is that each person appear in the sum for each of his friends. So in total there will be

friends of friends. Dividing by the total number of friends we get the average number of friends of friends F1

where V is the variance of the distribution of the number of friends. Since V is always positive, this conclude the proof that your friends have in average more friends than you do [8].

Some would say that if physicists are appreciated in the field network science it is because they are trained to such reasoning and possess the needed mathematical background to carry out the calculations. While it seems very unlikely in the light of my presentation, it nonetheless a possibility worth considering.

Anyway, even for experimental physicists there is a lesson here: a partial measurement may gives very biased results, not because the apparatus is bad, but because it looks at the problem from the wrong point.

Also, a socially gifted person would conclude on the even more general subject of everyday life experience, and how we should always search for objective and unbiased data, rather than using anecdotal example taken from our own experience to make decision. That would infuse a final touch of morality and wisdom to this blogpost. Readers would take a minute to meditate about the deep implications of the friendship paradox and about how physicists can use their mathematical training to help social science get to objective and solid results that could, maybe one day, change the world.

Obviously, if I was that kind of person, I would not have done my master thesis in the field of network science.

Benoît Richard

Notes

[1] I am interested to read any serious study of the subject, please send an email to ypf@sps.ch if you know any.

[2] Of course I made up this discussion, what exactly was you expecting by looking at this reference?

[3] Actually to be fair the first representation of social interactions as a network of nodes and edges is probably due to the psychiatrists J. L. Moreno and H. H. Jennings in their 1934 book Who shall survive?, where they studied the friendship network of a class of schoolchildren.

[4] To be socially ignorant is not the only possible way to achieve this, though. Being a psychopath is a valid alternative.

[5] One may assume that as a consequence network’s nodes love punk music. This is an open research question.

[6] I assume I am read by fellow physicists, who will most likely agree with this statement.

[7] As a person dot j is called Rachel, is 25 year old and a very successful software engineering graduate student looking forward to her first job. Beside she loves climbing and hiking. She would also hates the fact that all this information is irrelevant. But it is. Now get back in line, dot j.

[8] This effect sometimes referred as the friendship paradox, was first presented by the sociologist Scott L. Feld in 1991 in a paper named Why your friends have more friends than you do. Somehow, I think that the name of this paper fits well in the tone of this blogpost.

Serious references

Mentionned book and paper:

J. L. Moreno and H. H. Jennings. "Who shall survive?." (1934).

S. L. Feld. “Why your friends have more friends than you do”. In: American Journal of Sociology 96.6 (1991), pp. 1464–1477.

Data used to produce the thumbnail and title images have been retrieved from the Konect database:

J. Kunegis. “Konect: the Koblenz network collection”. In: Proceedings of the 22nd International Conference on World Wide Web. ACM. 2013, pp. 1343–1350.

These data originally appeared in the following papers:

P. M. Gleiser and L. Danon. “Community structure in jazz”. In: Advances in complex systems 6.04 (2003), pp. 565–573.

J.-F. Rual et al. “Towards a proteome-scale map of the human protein–protein interaction network”. In: Nature 437.7062 (2005), p. 1173.

Ana Roldan