The querelle between network science and the new social physics

Workshop 6

The new social physics• Revisited interest in the small world theory• Interested in the mathematical properties that allow a network

involving millions of nodes to be organized such that each is separated by an average of only six degrees from any other

• They claim to have identified a wide number of networks which manifest ‘small worldliness’, including the internet and the first completely mapped neural network, that of the nematode worm.

• However, the way in which new social physicists approach social networks lacks sociological purchase and evidences a superficial grasp of social relations/interactions

Nick Crossley, 2008, Small-World Networks, Complex Systems and Sociology, Sociology 42: 261

WattsHow can pairs of individuals, randomly selected from the USA’s enormous population, turn out to be connected by 6 degrees chain?• ‘small worldliness’ emerges in networks of any size, even if each

node has only a relatively small number of ties, if those ties are randomly assigned.

• if each of us is assumed (not unrealistically) to ‘know’ 500 people, and if each of the people we know knows a further 500 people, then we are connected to 250,000 people via only one intermediary (two degrees). Take that one step further by adding the 500 contacts of each of those we are connected to by our intermediary (three degrees) and the figure is 125,000,000, which is already much larger than the estimated 60,609,153 people who made up the UK population in 2006

• The obvious objection to this calculation concerns ‘redundancy’; many of our acquaintances would list one another as acquaintances and thus fail to reach out to new contacts.

But…• Network structures in the real world are not randomly

configured. And the way in which they are configured can run contrary to the prerequisites of small worldliness.

• Granovetter shows that individuals who are strongly tied to one another tend each to have further sets of strong ties to the same people. They are friends with their friends’ friends. In contrast to the small world situation, individuals are found to belong to small cliques or ‘clumps’ whose structure involves a high level of ‘redundancy’.

• Weak ties bridge cliques and provide pathways to new contacts. Social structure has a dual aspect. It consists of ‘clumps’ of strongly tied individuals, linked by weak ties

• It is these weak ties which provide for small worldliness in Watts’ view

Barabasi

• Watts’ model presupposes that all vertices in a small world network have the same number of contacts (‘degree’) or at least that degree is normally distributed.

• This is not necessarily so, however. In his work on the URL connectionscomprising the worldwide web, Barabási (2003) found a scale-free distribution of degree

• many nodes had a relatively small degree, whilst a small number had a very large degree.

• This network configuration generates a small world too, Barabási argues, because those vertices which enjoy a very high degree connect to most other vertices in the network, and this makes them hubs which connect up all or most of the other vertices in their network.

The small world thinkers tend to overlook important sociological factors. They ignore: • the meaning of social relations• the time–space relations that are central to social organization• the role of technology and transport in human relations• key issues of inequality, conflict and exclusion.

The lack of sociological theory“Almost anyone … is but a few removes from the President … but this is only true in terms of a particular mathematical viewpoint and does not, in any practical sense, integrate our lives with [his] … We should think of the two points as being not five persons apart but ‘five circles of acquaintances’ apart – five ‘structures’ apart. This helps to set it in its proper perspective”. (Milgram 2004[1967]: 117)• Milgram had good sociological reasons for conducting his experiments; he

sought to explore social closure and segregation.• However, if the small world problematic is to be sociologically relevant,

whether or not it deals with issues of closure and segregation, we need to move beyond artificial experiments centred upon ‘who knows whom’ to focus upon more meaningful and naturally occurring interactions in real life complex social systems.

A problem for sociology of science

Network science VS the new social physics: the querelle takes places in- Scientific publications- Twitter- SocnetThe problem: the physicists do not acknowledged the foundational work of SNA, which is never cited in their work

Example

Brian V. Carolan, The structure of educational research: The role of multivocality in promoting cohesion in an article interlock network, Social Networks 30 (2008) 69–82

Citations of• Sociological theorists• Network analysts• Physicists

Abbott, A., 2001. Chaos of Disciplines. University of Chicago Press, Chicago.Adamic, L.A., Huberman, B.A., 2002. Zipf’s Lawand the Internet. Glottometrics 3, 143–150.Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E., 2000. Classes of small-world networks. Proceedings of the National Academy of Sciences 97, 11149–11152.Barabasi, A.-L., 2003. Linked: How Everything is Connected to Everything Else and What it Means for Business, Science, and Everyday Life. Plume, Cambridge, MA.Barabasi, A.-L., Albert, R., Jeong, H., Bianconi, G., 2000. Power-law distribution of the World Wide Web. Science 287, 2115b.Batagelj, V., Mrvar, A., 2006. Pajek: Program for Analysis and Visualization of Large Networks (Version 1.14). Ljubljana, Slovenia.Bearman, P., 1993. Relations into Rhetorics: Local Elite Social Structure in Norfolk, England, 1540–1640. Rutgers University Press, New Brunswick, NJ.Borgatti, S.P., Everett, M.G., Shirey, P.R., 1990. LS Sets, Lamda Sets, and Other Cohesive Subsets. Social Networks 12, 337–357.Borner, K., Sanyal, S., Vespignani, A., 2007. Network science. In: Cronin, B. (Ed.), Annual Review of Information Science, vol. 41. American Society for Information Science and Technology, Medford, NJ, pp. 537– 607.Burt, R.S., 1982. Toward a Structural Theory of Action. Academic Press, New York.Burt, R.S., 1987. Social contagion and innovation: cohesion versus structural equivalence. American Journal of Sociology 92 (6), 1287–1335.Coleman, J.S., 1958. Relational analysis: the study of social organizations with survey methods. Human Organization 17, 28–36.Collins, B.E., Raven, B.H., 1968. Group structure: attraction, coalitions, communications and power. In: Lindzey, G., Aron, E. (Eds.), Handbook of Social Psychology. Addison-Wesley, MA.Crane, D., 1972. Invisible Colleges: Diffusion of Knowledge in Scientific Communities.University of Chicago Press, Chicago.de Nooy,W., Mrvar, A., Batagelj,V., 2005. Exploratory Social Network Analysis with Pajek. Cambridge University Press, New York.Doreian, P., Batagelj, V., Ferligoj, A.K., 2004. Generlized blockmodeling of two-mode network data. Social Networks 26 (1), 1–27.Durkheim, E., 1984. Division of Labor in Society (W.D. Walls, Trans.). The Free Press, New York.

Griffith, B.C., Mullins, N.C., 1972. Coherent social groups in scientific change: ‘invisible colleges’ may be consistent throughout science. Science 177, 959–964.Griswold, W., 1987. A methodological framework for the sociology of culture. Sociological Methodology 17, 1–35.Krackhardt, D., Stern, R.N., 1988. Informal networks and organizational crises: an experimental simulation. Social Psychology Quarterly 51 (2), 123– 140.Kuhn, T.S., 1962. The Structure of Scientific Revolutions. University of Chicago Press, Chicago.Merton, R.K., 1957. Social Theory and Social Structure. Free Press, Glencoe, IL.Merton, R.K., 1968. The Matthew Effect in Science. Science 159, 56–63.Milgram, S., 1967. The Small World Problem. Psychology Today 2, 60–67.Moody, J., 2004. The structure of a social science collaboration network: disciplinary cohesion from 1963–1999. American Sociological Review 69 (2), 213–238.Moody, J., White, D.R., 2003. Social cohesion and embeddedness: a hierarchical conception of social groups. American Sociological Review 68, 103– 127.Mulkay, M.J., 1974. Methodology in the sociology of science: some reflections on the study of radio astronomy. Social Science Information 13, 109–119.Mullins, N.C., Hargens, L.L., Hecht, P.K., Kick, E.L., 1977. The group structure of cocitation clusters: a comparative study. American Sociological Review 42 (4), 552–562.Newman, M.E.J., 2001. The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences 98, 404–409.Newman, M.E.J., 2004. Detecting community structure in networks. Eur. Phys. J. B 38, 321–330.Newman, M.E.J., Strogatz, S.H., Watts, D.J., 2001. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 1–19.Simmel, G., 1950. The Sociology of Georg Simmel (K. Wolff, Trans.). Free Press, Glencoe, IL.Small, H., Griffith, B.C., 1974. The structure of the scientific literature I. Science Studies 4, 17–40.Snijders, T.A.B., Borgatti, S.P., 1999. Non-parametric standard errors and tests for network statistics. Connections 22 (2), 161–170.Watts, D.J., 1999. Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton University Press, Princeton, NJ.

• Marco Tomassini, Leslie Luthi, Empirical analysis of the evolution of a scientific collaboration network, Physica A 385 (2007) 750–764

• Mingyang Wanga, Guang Yua, Daren Yua, Effect of the age of papers on the preferential attachment in citation networks, Physica A 388 (2009) 42734276

Example

[1] R. Albert, A.-L. Barabasi, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002) 47–97.[2] M.E.J. Newman, The structure and function of complex networks, SIAM Rev. 45 (2003) 167–256.[3] M.E.J. Newman, Clustering and preferential attachment in growing networks, Phys. Rev. E 64 (2001) 025102.[4] A.-L. Barabasi, H. Jeong, Z. Ne´da, E. Ravasz, A. Schubert, T. Vicsek, Evolution of the social network of scientific collaborations, Physica A 311 (2002) 590–614.[5] H. Jeong, Z. Ne´da, A.-L. Barabasi, Measuring preferential attachment in evolving networks, Europhysics Lett. 61 (2003) 567–572.[6] A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, J. Wiener, Graph structure in the web, Comput. Networks 33 (2000) 309–320.[7] A.-L. Baraba´ si, R. Albert, H. Jeong, Scale-free characteristics of random networks: the topology of the World Wide Web, Physica A 281 (2000) 69–77.[8] C.P. Massen, J.P.K. Doye, A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network, Physica A 377 (2007) 351–362.[9] G. Kossinets, D.J. Watts, Empirical analysis of an evolving social network, Science 311 (2006) 88–90.[10] A. Capocci, V.D.P. Servedio, F. Colaiori, L.S. Buriol, D. Donato, S. Leonardi, G. Caldarelli, Preferential attachment in the growth of social networks: the Internet encyclopedia Wikipedia, Phys. Rev. E 74 (2006) 036116.[11] L. Baraba´ si, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509–512.[12] P.L. Krapvsky, S. Redner, F. Leyvraz, Connectivity of growing random networks, Phys. Rev. Lett. 85 (2000) 4629–4632.[13] J.W. Grossman, The evolution of the mathematical research collaboration graph, Congress. Numer. 158 (2002) 201–212.[14] M.E.J. Newman, Scientific collaboration networks. I. Network construction and fundamental results, Phys. Rev. E 64 (2001) 016131.[15] M.E.J. Newman, Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality, Phys. Rev. E 64 (2001) 016132.[16] L. Luthi, M. Tomassini, M. Giacobini, W.B. Langdon, The genetic programming collaboration network and its communities, in: D. Thierens, et al. (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference GECCO’07, ACM Press, 2007,pp. 1643–1650.

Tomassini

[1] H. Zhu, X. Wang, J.-Y. Zhu, Phys. Rev. E 68 (2003) 056121.[2] S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 62 (2000) 1842.[3] L.A.N. Amaral, et al., Proc. Natl. Acad. Sci. USA 97 (2000) 11149.[4] K.B. Hajra, P. Sen, Phys. Rev. E 70 (2004) 056103.[5] K.B. Hajra, P. Sen, Physica A 346 (2005) 44.[6] K.B. Hajra, P. Sen, Physica A 368 (2006) 575.[7] D.J.S. Price, Science 149 (1965) 510.[8] S. Redner, Phys. Today 58 (2005) 49.[9] H. Jeong, Z. Déda, A.L. Barabási, Eur. Phys. Lett. 61 (2003) 567.[10] M.Y. Wang, G. Yu, D.R. Yu, Physica A 387 (2008) 4692.[11] B.C. Brooks, J. Documents 26 (1970) 283.

Wanga

Socnet

Date: Sun, 16 Jun 2013 03:34:33 -0400From: jcomas@BUCKNELL.EDUSubject: Re: [SOCNET] werent only the physicistsTo: SOCNET@LISTS.UFL.EDU

I don't have any data on popularity, but two tilts at the windmill here: 1. Watts book six degrees was part of this popularity and it is half about human behavior.2 the title six degrees resonated as it was embedded in the vulture ever since Milgram in the 1950s, boosted by the the John Guare play from the 1980s...turned into a film with Will smith. So, as to the wider public, it is possible the interest in SNA was stoked by many non physicist influences. Jordi

On Saturday, June 15, 2013, "Gulyás, László" wrote:Dear Barry and All,I think no one really questions that SNA existed before the arrival of the statistical physics approach to the field. Yet, it would be futile to question that it was the physicists' arrival that made it famous and known to the wider public (for better or worse).Best regards,Laszlo

2013.06.14. 21:53 Barry Wellman:I just sent this comment to Science Network analysis blossomed well before the physicists came lately to thefield in the 1990s. By the 1970s, social network analysis had aprofessional society with 700 members and a lively annual conference inthe U.S. or Europe. Much good research, theorizing and methods weredone, resulting in the current NSA activity, for better or worse. Thekey as you note, was the recent development of big data sets andcomputational ability to analyze them.

Barry Wellman

Twitter

Other publications

What is network science?ULRIK BRANDES, GARRY ROBINS, ANN McCRANIE and STANLEY WASSERMAN

Network Science / Volume 1 / Issue 01 / April 2013, pp 1 15DOI: 10.1017/nws.2013.2, Published online: 15 April 2013

As editors of a journal attempting to encompass a broad field with a long and storied history, we have already rejected the idea that network science “began” with some kind of new discovery or even a Kuhnian paradigm shift tipped off by work originating from physics, no matter how interesting or influential. Network science is neither tied to nor “owned” by any other field.We should not be ignorant of the forebears of our emerging science, and decades of empirical research. The past 15 years have seen a boom of interest in networks that does not overtly trace its roots to, for example, the sociometry of Moreno or the sociology of Simmel.