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Asymptotic distributions in random graphs with applications to social networks

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  • K. Nowicki

Abstract

Various kinds of subgraph counts have been proposed as important statistics in the social sciences: for instance, in connection with studies of the structural properties of social networks. Since the empirical structure in question often involves an element of randomness, subgraph counts are random variables and, consequently, we need to describe their probabilistic properties. In this paper we give a survey of results dealing with the asymptotic distributions of general subgraph counts for a number of standard graph distributions. Although we do not include proofs for all the results, we illustrate the methodology used through studies of asymptotic behaviour for certain subgraph counts.

Suggested Citation

  • K. Nowicki, 1991. "Asymptotic distributions in random graphs with applications to social networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(3), pages 295-325, September.
    • Handle: RePEc:bla:stanee:v:45:y:1991:i:3:p:295-325
    DOI: 10.1111/j.1467-9574.1991.tb01311.x
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    Cited by:

    1. Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel Density Estimation for Undirected Dyadic Data," Papers 1907.13630, arXiv.org.
    2. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    3. Graham, Bryan S. & Niu, Fengshi & Powell, James L., 2024. "Kernel density estimation for undirected dyadic data," Journal of Econometrics, Elsevier, vol. 240(2).
    4. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Knödler, D. & Dieterich, W., 1992. "Lattice-gas models of dispersive transport in disordered materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 426-432.
    6. Andersson, Pontus, 2000. "Small variance of subgraph counts in a random tournament," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 135-138, August.

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