Paper Critique: ‘Scale-free human migration and the geography of social networks’

Levy, M. (2010). Scale-free human migration and the geography of social networks. Physica A: Statistical Mechanics and Its Applications, 389(21), 4913–4917.

Levy (2010) is a widely published researcher from the Hebrew University of Jerusalem, specialising in economics, econometrics, and multidisciplinary studies. The author is published in a wide range of subject areas, and integrates mathematical modelling with descriptions of phenomena in social science. The paper contrasts scale-free networks with individuals’ physical location and geographic-distance interaction to online interactions. By analysing the spatial properties of social networks, Levy (2010, p. 4913) aims to expand the grounded theory concerning the “‘gravitational law of social interaction’, by which the probability of a social link decreases inversely with the square of the geographic distance.”

In exploring mobility, large-scale migration, and human movement, Levy (2010) demonstrates how migration may be explained using a power-law formula against the distance reported as a negative exponent. The researchers used migration patterns associated with 46.8 million individuals across the US. The paper notes that scale varies depending on daily dynamics, including work and recreational activities, against larger movements such as those incorporating global migrations and highly mobile individuals travelling across states and nations. Such human dynamics are demonstrated to determine the structure of social networks.

Levy (2010) analysed the US Census reports between 1995 and 2000. In the time frame, 3220 US counties are documented with the migration status of individuals moving between geographical locations. Such information is modelled using a series of network graph formulas. While the results are interesting, the author could also check the distinction between different types of network graphs, including small-world networks (Amaral et al., 2000) and random graph systems. The analysis would be more thorough if it extended into the mathematical modelling of graph dynamics, validating the dynamic as a small world in all instances and checking whether alternative graph structures have evolved (Klemm & Eguiluz, 2002).

The development of small-world networks and giant-node structures has been featured in a series of previous analyses of social networks (Goto et al., 2018). Consequently, the focus on an inverse distance law by Levy (2010, p. 4915) would be the strength of testing alternative network structures, either statistically rejecting the hypothesis of alternative network types or accepting that there could be an overlap or integration beyond a power-law fit.

From a perspective of human geography, the work aids in describing the patterns of human migration that occurred across the United States. As a probabilistic model, it allows large-scale policy decisions to be made based on mathematical structures of human movement. Over time, the proposed model would aid in probabilistic models fully describing migration phenomena and help develop government policy. Martin (2001) argued that geography is essential to public policy. Yet, “the impact of geography on the public policy realm has in general been disappointingly limited” (Martin, 2001, p. 191).

While Levy (2010) has provided a sound model, even disregarding the possibility of testing for small-world and other structures, the author has not investigated the use of such models in public policy analysis. The lack of public policy is unfortunate, as understanding social mobility and human-population dynamics is critical for government policy development (Blunt, 2007). In addition, Skeldon (1995) demonstrated how crucial awareness of human and population geography is from a political perspective. Hence, the concept developed by Levy (2010) could be strengthened by linking it to the policy issues of human mobility.


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(21), 11149–11152.

Blunt, A. (2007). Cultural geographies of migration: Mobility, transnationality and diaspora. Progress in Human Geography, 31(5), 684–694.

Goto, H., Viegas, E., Jensen, H. J., Takayasu, H., & Takayasu, M. (2018). Smoluchowski Equation for Networks: Merger Induced Intermittent Giant Node Formation and Degree Gap. Journal of Statistical Physics, 172(4), 1086–1100.

Klemm, K., & Eguiluz, V. M. (2002). Growing scale-free networks with small-world behavior. Physical Review E, 65(5), 057102.

Levy, M. (2010). Scale-free human migration and the geography of social networks. Physica A: Statistical Mechanics and Its Applications, 389(21), 4913–4917.

Martin, R. (2001). Geography and public policy: The case of the missing agenda. Progress in Human Geography, 25(2), 189–210.

Skeldon, R. (1995). The challenge facing migration research: A case for greater awareness. Progress in Human Geography, 19(1), 91–96.

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