Skip to main content

Advertisement

Springer Nature Link
Log in

Generating and analyzing spatial social networks

  • Manuscript
  • Published:
Computational and Mathematical Organization Theory Aims and scope Submit manuscript

Abstract

In this paper, we propose a class of models for generating spatial versions of three classic networks: Erdös-Rényi (ER), Watts-Strogatz (WS), and Barabási-Albert (BA). We assume that nodes have geographical coordinates, are uniformly distributed over an m × m Cartesian space, and long-distance connections are penalized. Our computational results show higher clustering coefficient, assortativity, and transitivity in all three spatial networks, and imperfect power law degree distribution in the BA network. Furthermore, we analyze a special case with geographically clustered coordinates, resembling real human communities, in which points are clustered over k centers. Comparison between the uniformly and geographically clustered versions of the proposed spatial networks show an increase in values of the clustering coefficient, assortativity, and transitivity, and a lognormal degree distribution for spatially clustered ER, taller degree distribution and higher average path length for spatially clustered WS, and higher clustering coefficient and transitivity for the spatially clustered BA networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Alam SJ, Geller A (2012) Networks in Agent-based Social Simulation. In: Heppenstall A, Crooks AT, See LM, Batty M (eds) Agent-based models of geographical systems. Springer, New York, pp 199–218

    Chapter  Google Scholar 

  • Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47

    Article  Google Scholar 

  • Albert R, Jeong H, Barabási AL (1999) Internet: Diameter of the world-wide web. Nat 401(6749):130–131

    Article  Google Scholar 

  • Alizadeh M, Coman A, Lewis M, Cioffi-Revilla C (2014) Intergroup conflict escalation leads to more extremism. J Artif Soc Soc Simul 17(4):4

    Article  Google Scholar 

  • Alizadeh M, Cioffi-Revilla C, Crooks A (2015) The effect of in-group favoritism on the collective behavior of individuals'opinions. Adv Complex Syst 18(01n02):1550002

    Article  Google Scholar 

  • Barabasi A-L, Albert R (1999) Emergence of Scaling in Random Networks. Science New Ser 286(5439):509–512

    Google Scholar 

  • Barthélemy M (2003) Crossover from scale-free to spatial networks. Europhys Lett 63(6):915

    Article  Google Scholar 

  • Barthélemy M (2011) Spatial networks. Phys Rep 499(1):1–101

    Article  Google Scholar 

  • Batty M (2012) The new science of cities. MIT Press, Cambridge

    Google Scholar 

  • Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308

    Article  Google Scholar 

  • Borgatti S, Everett MG, Johnson JC (2013) Analyzing social networks. Sage, Los Angeles

    Google Scholar 

  • Bretagnolle A, Pumain D (2010) Simulating urban networks through multiscalar space-time dynamics (Europe and United States, 17th–20th centuries). Urban Studies 47(13):2819–2839

    Article  Google Scholar 

  • Bruggeman J (2008) Social networks. Routledge, London

    Google Scholar 

  • Callaway DS, Hopcroft JE, Kleinberg JM, Newman MEJ, Strogatz SH (2001) Are randomly grown graphs really random? Phys Rev E 64:041902

    Article  Google Scholar 

  • Chung F, Lu L (2002) The average distances in random graphs with given expected degrees. Proc Natl Acad Sci USA 99:15879–15882

    Article  Google Scholar 

  • Cioffi-Revilla C (2014) Introduction to computational social science: principles and applications. Springer, London

    Book  Google Scholar 

  • Cioffi-Revilla C (2015) A unified framework for convergence of social, engineering, and natural sciences. In: Bainbridge WS, Roco MC (eds) Handbook of science and technology convergence. Springer, London (in preparation)

  • Clauset A, Shalizi CR, Newman ME (2009) Power-law distributions in empirical data. SIAM review 51(4):661–703

    Article  Google Scholar 

  • Cointet JP, Roth C (2007) How realistic should knowledge diffusion models be?. J Artif Soc Soc Simul 10(3):5

    Google Scholar 

  • Dorogovtsev SN, Mendes JFF (2002) Evolution of networks. Adv Phys 51:1079–1187

    Article  Google Scholar 

  • Ducruet C, Beauguitte L (2013) Spatial science and network science: review and outcomes of a complex relationship. Netw Spat Econ 14(3–4):1–20

    Google Scholar 

  • Edmonds B (2006) How are physical and social spaces related? In: Billari FC, Fent T, Prskawetz A, Scheffran J (eds) Agent-based computational modelling. Springer, New York. (Downloaded on 10 March 08 from http://cfpm.org/cpmrep127.html)

  • Erdös P, Rényi A (1959) On random graphs. Publ Math 6:290–297

    Google Scholar 

  • Erdös P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–61

    Google Scholar 

  • Fischer CS (1982) To dwell among friends. University of Chicago Press, Chicago

    Google Scholar 

  • Garfield E (1979) It’s a small world after all. Curr Contents 43:5–10

    Google Scholar 

  • Gilbert EN (1959) Random graphs. Ann Math Stat 30:1141–1144

    Article  Google Scholar 

  • Gilbert N (2006) Putting the social into social simulation. Keynote address to the first world social simulation conference, Kyoto

  • Hamill L, Gilbert N (2009) Social circles: a simple structure for agent-based social network models. J Artif Soc Soc Simul 12(2):3

    Google Scholar 

  • Holzhauer S, Krebs F, Ernst A (2013) Considering baseline homophily when generating spatial social networks for agent-based modelling. Comput Math Org Theory 19(2):128–150

    Article  Google Scholar 

  • Kleinberg JM (2000) Navigation in a small world. Nature 406:845

    Article  Google Scholar 

  • Klemm K, Eguiluz VM (2002) Growing scale-free networks with small-world behavior. Phys Rev E 65(5):057102

    Article  Google Scholar 

  • Lambiotte R, Blondel VD, de Kerchove C, Huens E, Prieur C, Smoreda Z, Van Dooren P (2008) Geographical dispersal of mobile communication networks. Physica A 387(21):5317–5325

    Article  Google Scholar 

  • Latane B, Liu JH, Nowak A, Bonevento M, Zheng L (1995) Distance matters: physical space and social impact. Pers Soc Psychol Bull 21(8):795–805

    Article  Google Scholar 

  • Manna SS, Sen P (2002) Modulated scale-free network in Euclidean space. Phys Rev E 66(6):066114

    Article  Google Scholar 

  • Milgram S (1967) The small world problem. Psychol Today 2:60–67

    Google Scholar 

  • Modarres M, Kaminskiy M, Krivtsov V (2010) Reliability engineering and risk analysis: a proctical guide, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  • Myers A (2010) Complex system reliability: multichannel systems with imperfect fault coverage, 2nd edn. Springer, London

    Book  Google Scholar 

  • Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89(20):208701

    Article  Google Scholar 

  • Newman MEJ (2003a) Mixing patterns in networks. Phys Rev E 67:026126

    Article  Google Scholar 

  • Newman MEJ (2003b) The structure and function of complex networks. SIAM Rev 45(2):167–256

    Article  Google Scholar 

  • Newman MEJ (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69:066133

    Article  Google Scholar 

  • Newman MEJ (2005) Power laws, Pareto distributions and Zipf's law. Contemp phys 46(5):323–351

    Article  Google Scholar 

  • Onnela JP, Arbesman S, Gonzalez MC, Barabási AL, Christakis NA (2011) Geographic constraints on social network groups. PLoS One 6(4):e16939

    Article  Google Scholar 

  • Rapoport A (1957) Contribution to the theory of random and biased nets. Bull Math Biophys 19:257–277

    Article  Google Scholar 

  • Redner S (1998) How popular is your paper? An empirical study of the citation distribution. Eur Phys J B 4:131–134

    Article  Google Scholar 

  • Soboll A, Elbers M, Barthel R, Schmude J, Ernst A, Ziller R (2011) Integrated regional modelling and scenario development to evaluate future water demand under global change conditions. Mitig Adapt Strateg Glob Change 16(4):477–498

    Article  Google Scholar 

  • Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2):307–333

    Article  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:4

    Article  Google Scholar 

  • Wong LH, Pattison P, Robins G (2006) A spatial model for social networks. Physica A 360:99–120

    Article  Google Scholar 

  • Xulvi-Brunet RI, Sokolov M (2002) Evolving networks with disadvantaged long-range connections. Phys Rev E 66(2):026118

    Article  Google Scholar 

  • Yook S-H, Jeong H, Barabási A-L (2002) Modeling the Internet’s large-scale topology. Proc Natl Acad Sci 99(21):13382–13386

    Article  Google Scholar 

  • Yoshida T, Tomizawa N, Gotoh T, Iguchi H, Sugioka K, Ikeda, KI (2008) Consumer phase shift simulation based on social psychology and complex networks. In: 2008 IEEE Congress on Services-Part I, pp 289–296

Download references

Acknowledgments

This study was supported in part by the Center for Social Complexity and the Computational Social Science program within the Department of Computational and Data Sciences at George Mason University. M. Alizadeh is funded by a GMU Presidential Fellowship and, together with C. Cioffi-Revilla, by ONR-Minerva Grant No. N00014130054.

Author information

Authors and Affiliations

  1. Computational Social Science Program, Department of Computational and Data Sciences, George Mason University, Fairfax, VA, USA

    Meysam Alizadeh, Claudio Cioffi-Revilla & Andrew Crooks

  2. Center for Social Complexity, Krasnow Institute for Advanced Studies, George Mason University, Fairfax, VA, USA

    Meysam Alizadeh, Claudio Cioffi-Revilla & Andrew Crooks

Authors
  1. Meysam Alizadeh
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Claudio Cioffi-Revilla
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Andrew Crooks
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Meysam Alizadeh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alizadeh, M., Cioffi-Revilla, C. & Crooks, A. Generating and analyzing spatial social networks. Comput Math Organ Theory 23, 362–390 (2017). https://doi.org/10.1007/s10588-016-9232-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10588-016-9232-2

Keywords