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Mathematical Modeling and Inference for Degree-capped Ego-centric Network Sampling

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  • Fotouhi, Babak
  • Rytina, Steven

Abstract

The structure of social networks is usually inferred from limited sets of observations via suitable network sampling designs. In offline social network sampling, for practical considerations, researchers sometimes build in a cap on the number of social ties any respondent may claim. It is commonly known in the literature that using a cap on the degrees begets methodologically undesirable features because it discards information about the network connections. In this paper, we consider a mathematical model of this sampling procedure and seek analytical solutions to recover some of the lost information about the underlying network. We obtain closed-form expressions for several network statistics, including the first and second moments of the degree distribution, network density, number of triangles, and clustering. We corroborate the accuracy of these estimators via simulated and empirical network data. Our contribution highlights notable room for improvement in the analysis of some existing social network data sets.

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  • Fotouhi, Babak & Rytina, Steven, 2018. "Mathematical Modeling and Inference for Degree-capped Ego-centric Network Sampling," SocArXiv 5kez8, Center for Open Science.
    • Handle: RePEc:osf:socarx:5kez8
    DOI: 10.31219/osf.io/5kez8
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    1. Raghuram Iyengar & Christophe Van den Bulte & Thomas W. Valente, 2011. "Opinion Leadership and Social Contagion in New Product Diffusion," Marketing Science, INFORMS, vol. 30(2), pages 195-212, 03-04.
    2. Scott D. McClurg, 2006. "The Electoral Relevance of Political Talk: Examining Disagreement and Expertise Effects in Social Networks on Political Participation," American Journal of Political Science, John Wiley & Sons, vol. 50(3), pages 737-754, July.
    3. Fujimoto, Kayo & Valente, Thomas W., 2015. "Multiplex congruity: Friendship networks and perceived popularity as correlates of adolescent alcohol use," Social Science & Medicine, Elsevier, vol. 125(C), pages 173-181.
    4. J. D. Noh, 2008. "Loop statistics in complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(2), pages 251-257, November.
    5. A James O’Malley & Samuel Arbesman & Darby Miller Steiger & James H Fowler & Nicholas A Christakis, 2012. "Egocentric Social Network Structure, Health, and Pro-Social Behaviors in a National Panel Study of Americans," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    6. Lakon, Cynthia M. & Ennett, Susan T. & Norton, Edward C., 2006. "Mechanisms through which drug, sex partner, and friendship network characteristics relate to risky needle use among high risk youth and young adults," Social Science & Medicine, Elsevier, vol. 63(9), pages 2489-2499, November.
    7. Coren L. Apicella & Frank W. Marlowe & James H. Fowler & Nicholas A. Christakis, 2012. "Social networks and cooperation in hunter-gatherers," Nature, Nature, vol. 481(7382), pages 497-501, January.
    8. Lynne McCallister & Claude S. Fischer, 1978. "A Procedure for Surveying Personal Networks," Sociological Methods & Research, , vol. 7(2), pages 131-148, November.
    9. Michell, Lynn & Amos, Amanda, 1997. "Girls, pecking order and smoking," Social Science & Medicine, Elsevier, vol. 44(12), pages 1861-1869, June.
    10. Schaefer, D.R. & Simpkins, S.D., 2014. "Using social network analysis to clarify the role of obesity in selection of adolescent friends," American Journal of Public Health, American Public Health Association, vol. 104(7), pages 1223-1229.
    11. Benjamin Cornwell & L. Philip Schumm & Edward O. Laumann & Jessica Graber, 2009. "Social Networks in the NSHAP Study: Rationale, Measurement, and Preliminary Findings," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 64(suppl_1), pages 47-55.
    12. Valente, Thomas W. & Watkins, Susan C. & Jato, Miriam N. & Van Der Straten, Ariane & Tsitsol, Louis-Philippe M., 1997. "Social network associations with contraceptive use among Cameroonian women in voluntary associations," Social Science & Medicine, Elsevier, vol. 45(5), pages 677-687, September.
    13. Katherine L. Fiori & Jacqui Smith & Toni C. Antonucci, 2007. "Social Network Types Among Older Adults: A Multidimensional Approach," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 62(6), pages 322-330.
    14. Nekovee, M. & Moreno, Y. & Bianconi, G. & Marsili, M., 2007. "Theory of rumour spreading in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 457-470.
    15. Choi, K.-H. & Paul, J. & Ayala, G. & Boylan, R. & Gregorich, S.E., 2013. "Experiences of discrimination and their impact on the mental health among African American, Asian and Pacific Islander, and Latino men who have sex with men," American Journal of Public Health, American Public Health Association, vol. 103(5), pages 868-874.
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