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Social ties, homophily and extraversion--introversion to generate complex networks

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Abstract

Many interconnected systems and particularly social interactions can be modeled as networks. These networks often exhibit common properties such as high clustering coefficient, low average path lengths and degree distributions following power-law. Networks having these properties are called small world-scale free networks or simply complex networks. Recent interest in complex networks has catalysed the development of algorithmic models to artificially generate these networks. Often these algorithms introduce network properties in the model regardless of their social interpretation resulting in networks which are statistically similar but structurally different from real world networks. In this paper, we focus on social networks and apply concepts of social ties, homophily and extraversion-introversion to develop a model for social networks with small world and scale free properties. We claim that the proposed model produces networks which are structurally similar to real world social networks.

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Notes

  1. NetScience Network is a co-authorship network of scientists working on network theory and experiments, as compiled by Newman in May (2006). The biggest connected component is considered for visualization here which contains 379 nodes and 914 edges.

References

  • Auber D (2003) Tulip—a huge graph visualization framework. In: Mutzel P, Jünger M (eds) Graph drawing software, mathematics and visualization series. Springer, Berlin

  • Badham J, Stocker R (2010) A spatial approach to network generation for three properties: degree distribution, clustering coefficient and degree assortativity. J Artif Soc Soc Simul 13(1):11

    Google Scholar 

  • Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512

    Article  MathSciNet  Google Scholar 

  • Boguñá M, Pastor-Satorras R, Díaz-Guilera A, Arenas A (2004) Models of social networks based on social distance attachment. Phys Rev E 70(5):056122

    Article  Google Scholar 

  • Bollobás B, Riordan OM (2002) Mathematical results on scale-free random graphs. In: Bornholdt S, Schuster HG (eds) Handbook of Graphs and Networks: From the Genome to the Internet. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi:10.1002/3527602755.ch1

  • Bollt EM, ben Avraham D (2004) What is special about diffusion on scale-free nets? New J Phys 7:26

    Article  Google Scholar 

  • Bourqui R, Zaidi F, Gilbert F, Sharan U, Simonetto P (2008) Vast 2008 challenge: social network dynamics using cell phone call patterns. In: IEEE symposium on visual analytics science and technology, 2008

  • Burt RS (2005) Brokerage and closure. Oxford University Press, Oxford

    Google Scholar 

  • Cannataro M, Guzzi PH, Veltri P (2010) Protein-to-protein interactions: technologies, databases, and algorithms. ACM Comput Surv 43:1:1–1:36

    Article  Google Scholar 

  • Catanzaro M, Caldarelli G, Pietronero L (2004) Assortative model for social networks. Phys Rev E (Statistical, Nonlinear, and Soft Matter Physics) 70(3):1–4

    Google Scholar 

  • Condon A, Karp RM (1999) Algorithms for graph partitioning on the planted partition model. Random Struct Algorithms 18(2):116–140

    Article  MathSciNet  Google Scholar 

  • de Almeida ML, Mendes GA, Viswanathan GM, da Silva LR (2013) Scale-free homophilic network. Europ Phys J B 86(2):1–6

    Article  Google Scholar 

  • Dorogovtsev S, Mendes J (2000) Exactly solvable small-world network. Europ Phys Lett 50(1):1–7

    Article  Google Scholar 

  • Dorogovtsev SN, Mendes JFF (2000) Evolution of networks with aging of sites. Phys Rev E 62(2):1842–1845

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ducruet C, Zaidi F (2012) Maritime constellations: a complex network approach to shipping and ports. Maritime Policy Manag 39(2):151–168

    Article  Google Scholar 

  • Fortunato S (2010) Community detection in graphs. Phys Rep 486(3):75–174

    Article  MathSciNet  Google Scholar 

  • Frank O, Strauss D (1986) Markov graphs. J Am Stat Assoc 81(395):832–842

    Article  MathSciNet  MATH  Google Scholar 

  • Fu P, Liao, K (2006) An evolving scale-free network with large clustering coefficient. In ICARCV IEEE, pp 1–4

  • Geng X, Wang Y (2009) Degree correlations in citation networks model with aging. Europhys Lett 88(3):38002

    Article  MathSciNet  Google Scholar 

  • Goldenberg A, Zheng AX, Fienberg SE, Airoldi EM (2010) A survey of statistical network models. Found Trends Mach Learn 2(2):129–233

    Article  Google Scholar 

  • Granovetter M (1973) The strength of weak ties. Am J Sociol 78(6):1360–1380

    Article  Google Scholar 

  • Guillaume J-L, Latapy M (2006) Bipartite graphs as models of complex networks. Phys A Stat Mech Appl 371(2):795–813

    Article  Google Scholar 

  • Guimera R, Mossa S, Turtschi A, Amaral LAN (2005) The worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. Proc Nat Acad Sci USA 102(22):7794–7799

    Article  MathSciNet  MATH  Google Scholar 

  • Holme P, Kim BJ (2002) Growing scale-free networks with tunable clustering. Phys Rev E 65:026107

    Article  Google Scholar 

  • Hussain OA, Anwar Z, Saleem S, Zaidi F (2013) Empirical analysis of seed selection criterion in influence mining for different classes of networks. In: Cloud and green computing (CGC), 2013 third international conference on IEEE, pp 348–353

  • Jackson MO (2005) A survey of network formation models: stability and efficiency. Cambridge University Press, Cambridge

    Google Scholar 

  • Jung CJ (1921) Psychologischen typen, volume Translation H.G. Baynes, 1923. Rascher Verlag, Zurich

  • Kasturirangan R (1999) Multiple scales in small-world networks. In Brain and Cognitive Science Department, MIT

    Google Scholar 

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

    Article  Google Scholar 

  • Krackhardt D (1992) The strength of strong ties: the importance of philos in networks and organization. In: Nohria N, Eccles RG (eds) Networks and organizations. Harvard Business School Press, Boston

  • Krivitsky PN, Handcock MS, Raftery AE, Hoff PD (2009) Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Soc Netw 31(3):204–213

    Article  Google Scholar 

  • Kurant M, Gjoka M, Butts CT, Markopoulou (2011) Walking on a graph with a magnifying glass: stratified sampling via weighted random walks. In: Proceedings of the ACM SIGMETRICS joint international conference on measurement and modeling of computer systems, pp 281–292. ACM

  • Lancichinetti A, Fortunato S (2009) Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys Rev E 80(1):016118

    Article  Google Scholar 

  • Lewis K, Kaufman J, Gonzalez M, Wimmer A, Christakis N (2008) Tastes, ties, and time: a new social network dataset using facebook.com. Soc Netw 30(4):330–342

    Article  Google Scholar 

  • Liu J-G, Dang Y-Z, Wang Z (2005) Multistage random growing small-world networks with power-law degree distribution. Chin Phys Lett 3(3):746

    Google Scholar 

  • Moriano P, Finke J (2013) On the formation of structure in growing networks. arXiv preprint arXiv:1301.4192

  • Newman MEJ (2001) Scientific collaboration networks. I. Network construction and fundamental results. Phys Rev E 64(1):016131. doi:10.1103/PhysRevE.64.016131

  • Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett, pp 89–20

  • Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104

  • Newman MEJ, Watts DJ, Strogatz SH (2002) Random graph models of social networks. Proc Natl Acad Sci USA 99(Suppl 1):2566–2572

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Pan Z, Li X, Wang X (2006) Generalized local-world models for weighted networks. Phys Rev E 73(5):056109

    Article  Google Scholar 

  • Pasta MQ, Jan Z, Sallaberry A, Zaidi F (2013) Tunable and growing network generation model with community structures. In: social computing and applications, 2013 third international conference on, pp 233–240

  • Pasta MQ, Zaidi F, Rozenblat C (2014) Generating online social networks based on socio-demographic attributes. J Complex Netw 2(4):475–494

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

    Article  MathSciNet  Google Scholar 

  • Rapoport A, Horvath WJ (1961) A study of a large sociogram. Behav Sci 6(4):279–291

    Article  Google Scholar 

  • Robins G, Pattison P, Kalish Y, Lusher D (2007) An introduction to exponential random graph (p) models for social networks. Soc Net 29(2):173–191

    Article  Google Scholar 

  • Sallaberry A, Zaidi F, Melançon G (2013) Model for generating artificial social networks having community structures with small-world and scale-free properties. Soc Netw Anal Min 3:597–609

    Article  Google Scholar 

  • Schnettler S (2009) A structured overview of 50 years of small-world research. Soc Netw 31(3):165–178

    Article  Google Scholar 

  • Scott JP (2000) Social network analysis: a handbook. SAGE Publications, London

    Google Scholar 

  • Scott J (2011) Social network analysis: developments, advances, and prospects. Soc Net Anal Min 1:21–26

    Article  Google Scholar 

  • Simmel G, Wolff KH (1950) The sociology of Georg Simmel / translated and edited with an introduction by Kurt H. Wolff. Free Press, Glencoe Ill

    Google Scholar 

  • Snijders TA, Pattison PE, Robins GL, Handcock MS (2006) New specifications for exponential random graphs models. Sociolog Methodol 36(1):99–153

    Article  Google Scholar 

  • Sun X, Feng E, Li J (2007) From unweighted to weighted networks with local information. Phys A Stat Mech Appl 385(1):370–378

    Article  Google Scholar 

  • Toivonen R, Kovanen L, Kivel M, Onnela J-P, Saramki J, Kaski K (2009) A comparative study of social network models: network evolution models and nodal attribute models. Soc Netw 31(4):240–254

    Article  Google Scholar 

  • Virtanen S (2003) Properties of nonuniform random graph models. Research Report A77, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland

  • Wang L-N, Guo J-L, Yang H-X, Zhou T (2009) Local preferential attachment model for hierarchical networks. Phys A Stat Mech Appl 388(8):1713–1720

    Article  Google Scholar 

  • Wang J, Rong L (2008) Evolving small-world networks based on the modified ba model. Computer science and information technology, international conference on, pp 143–146

  • Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393:440–442

    Article  Google Scholar 

  • Wattsc DJ (2003) Six degrees: the science of a connected age, 1st edn. W. W. Norton & Company, New York

    Google Scholar 

  • Wen G, Duan Z, Chen G, Geng X (2011) A weighted local-world evolving network model with aging nodes. Phys A Stat Mech Appl 390(21):4012–4026

    Article  Google Scholar 

  • Wong LH, Pattison P, Robins G (2006) A spatial model for social networks. Phys A Stat Mech Appl 360(1):99–120

    Article  Google Scholar 

  • Zaidi F (2013) Small world networks and clustered small world networks with random connectivity. Soc Netw Anal Min 3(1):51–63

    Article  Google Scholar 

  • Zhu H, Wang X, Zhu J-Y (2003) Effect of aging on network structure. Phys Rev E 68(5):056121

    Article  Google Scholar 

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Authors and Affiliations

  1. Levich Institute and Physics Department, City College of New York, New York, NY, USA

    Faraz Zaidi

  2. Karachi Institute of Economics and Technology, Karachi, Pakistan

    Faraz Zaidi & Muhammad Qasim Pasta

  3. Usman Institute of Technology, Karachi, Pakistan

    Muhammad Qasim Pasta

  4. LIRMM, Université Paul Valéry Montpellier, Montpellier, France

    Arnaud Sallaberry

  5. CNRS UMR 5800 LaBRI, Talence, France

    Guy Melançon

  6. INRIA Bordeaux – Sud-Ouest, Talence, France

    Guy Melançon

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  1. Faraz Zaidi
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  2. Muhammad Qasim Pasta
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  3. Arnaud Sallaberry
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  4. Guy Melançon
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Correspondence to Faraz Zaidi.

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Zaidi, F., Pasta, M.Q., Sallaberry, A. et al. Social ties, homophily and extraversion--introversion to generate complex networks. Soc. Netw. Anal. Min. 5, 29 (2015). https://doi.org/10.1007/s13278-015-0270-4

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  • DOI: https://doi.org/10.1007/s13278-015-0270-4

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