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a network theory of everything?

Omar 

The latest issue of the journal Neural Networks has an interesting article  dealing with topological similarities between neural networks and social networks.  The authors find that neural networks tend to be similar to friendship networks based on the “liking” relationship (they exhibit a statistically disproportionate number of closed-in triads).  In particular “balanced” triads are much more likely to be found than imbalanced triads (see Davis 1963, for an influential sociological elaboration of Heider’s notion of balance).  The authors conclude (p. 20) with the claim that,

In summary, explicit social attitudes were found to crucially affect the contents of local structures in social networks, and an unexpected topological similarity between mammalian cortical networks and social friendship networks was reported. In these two systems, balanced reciprocal connections seem to be positively selected compared with random networks. Because it is unlikely that each actor directly obtains global information about the network topology, each actor is apt to establish connections to more attractive actors rather than less attractive ones, resulting in an abundance of clique and balanced structures. Together with the importance of information processing in brain and friendship networks, our findings suggest that these two networks developed and evolved on the basis of common principles, such as attractive interaction, in order to achieve similar purposes.*

Ever since physicists began to be interested in networks, a small cottage industry has grown around the notion of finding structural similarities across wide ranges of biotic, artificial, molecular, cross-species, social, geographical, etc., networks.  Comte and Saint Simon would be proud:  the aim is nothing short of coming up with abstract “laws” of network organization that transcend levels of organization and material substrates.  One early candidate for such a law is the “power law,” or the empirical generalization that in-degree (i.e. number of people that choose you as a friend) is distributed among nodes in a network according to P(Ni=k)~k^-gamma, where P(Ni=k) is the expected probability that node Ni has and in-degree (or out-degree) of k and gamma is some constant to be derived from an analytical model or to be estimated from the data (which usually hovers around little over the magic number 2–mostly between 2.1 and 2.5–across an impressive variety of networks).

My sense is that regardless of the shiny credentials that this approach comes certified with (i.e. physicists like it), there are diminishing returns to this notion that the same “laws of of network organization” govern the formation of all networks, social or non-social, human or animal, molecular or neural.  What has happened is that researchers are content just to show that the law “holds” in yet another type of network, yet are skimpy in providing generative mechanisms that might explain why this is so (some early candidates for this type of generative mechanism, such as “preferential attachment” have been proposed, but they remain woefully underspecified:  for human networks there could be plausible social-psychological micro-mechanisms–people like popular people, and popularity is a self-fulfilling prophecy–but it is hard to see how this translates to other types of networks where the mechanisms would surely have to be different, or the notion of preferential attachment would be merely metaphorical as molecules don’t have a social psychology).

My sense is that after the faddishness of finding yet another example of how the “general” laws of network organization obtain for yet another domain wears off, (and the cottage industry of short papers falls under the curse of overproduction) people are going to start to worry about the truly hard scientific questions here.  In other words, lazy covering law style of explanation will no longer do, and will have to give way to true mechanismic and generative explanations of these regularities, each of which is going to have to deal with the specificities of network formation in each realm:  a human is not a molecule is not a power-plant is not a neuron is not city.  Repeat after me…

*This type of generalized functionalism reminds one of the late Parsons of Action theory and the human condition.

Written by Omar

February 3, 2007 at 2:27 pm

6 Responses

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  1. a human is not a molecule is not a power-plant is not a neuron is not city. Repeat after me…

    If I remember right (it was a long time ago) there are substantial chunks of Spencer’s Social Dynamics where he elaborates on just this analogy — telegraph wires as nerves, roads as blood vessels and all that. Interstates aren’t called “arteries” by accident.

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    Kieran

    February 3, 2007 at 3:00 pm

  2. Looks like you got your work cut out for you. Have at it.

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    moreno

    February 3, 2007 at 3:48 pm

  3. […] while ago, I complained about the trend among natural scientists who study networks to write papers suggesting vague general […]

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  4. […] a previous post, I have expressed my dissatisfaction regarding this approach to the study of network phenomena.  […]

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  5. […] are a few old posts by Omar (here, here, and here) about the “new science” of […]

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  6. You’re right to the extent that finding power law dependence is only the beginning rather than the end of explaining network structure. There are many ways in which power law dependence can arise, some less profound than others. Still, mirror neurons give one tangible reason not to discount the insights that neural networks might provide into social networks (and vice versa). Hayek sort of proved this point writing *Sensory Order*, at least to my mind n

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    Michael F. Martin

    May 22, 2009 at 1:41 am


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