A note on asymptotic distributions in a directed network model with degree heterogeneity and homophily

References

• Bader, G. D., and C. W. Hogue. 2003. An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics 4 (1):2. doi:10.1186/1471-2105-4-2.
   PubMed Web of Science ®Google Scholar
• Barabási, A.-L., and E. Bonabeau. 2003. Scale-free networks. Scientific American 288 (5):60–9. doi:10.1038/scientificamerican0503-60.
   PubMed Web of Science ®Google Scholar
• Billingsley, P. 1999. Convergence of probability measures. New York, NY: John Wiley & Sons, Inc. ISBN 0-471-19745-9.
   Google Scholar
• Chatterjee, S., P. Diaconis, and A. Sly. 2011. Random graphs with a given degree sequence. The Annals of Applied Probability 21 (4):1400–1435. doi:10.1214/10-AAP728.
   Web of Science ®Google Scholar
• Chen, M., K. Kato, and C. Leng. 2019. Analysis of networks via the sparse β-model. arXiv Preprint arXiv:1908.03152.
   Google Scholar
• Emirbayer, M., and J. Goodwin. 1994. Network analysis, culture, and the problem of agency. American Journal of Sociology 99 (6):1411–54. doi:10.1086/230450.
   Web of Science ®Google Scholar
• Fan, Y., H. Zhang, and T. Yan. 2020. Asymptotic theory for differentially private generalized β-models with parameters increasing. Statistics and Its Interface 13 (3):385–98. doi:10.4310/SII.2020.v13.n3.a8.
   Web of Science ®Google Scholar
• Fellows, I., and M. S. Handcock. 2012. Exponential-family random network models. arXiv Preprint arXiv:1208.0121.
   Google Scholar
• Fienberg, S. E. 2012. A brief history of statistical models for network analysis and open challenges. Journal of Computational and Graphical Statistics 21 (4):825–39. doi:10.1080/10618600.2012.738106.
   Web of Science ®Google Scholar
• Girvan, M., and M. E. Newman. 2002. Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America 99 (12):7821–6. doi:10.1073/pnas.122653799.
   PubMed Web of Science ®Google Scholar
• Graham, B. S. 2017. An econometric model of network formation with degree heterogeneity. Econometrica 85 (4):1033–63. doi:10.3982/ECTA12679.
   Web of Science ®Google Scholar
• Granovetter, M. 1985. Economic action and social structure: The problem of embeddedness. American Journal of Sociology 91 (3):481–510. doi:10.1086/228311.
   Web of Science ®Google Scholar
• Hillar, C., and A. Wibisono. 2013. Maximum entropy distributions on graphs. arXiv Preprint arXiv:1301.3321.
   Google Scholar
• Karwa, V., and A. Slavković. 2016. Inference using noisy degrees: Differentially private beta-model and synthetic graphs. The Annals of Statistics 44 (1):87–112. doi:10.1214/15-AOS1358.
   Web of Science ®Google Scholar
• Kossinets, G., and D. J. Watts. 2006. Empirical analysis of an evolving social network. Science (New York, N.Y.) 311 (5757):88–90. doi:10.1126/science.1116869.
   PubMed Web of Science ®Google Scholar
• Loève, M. 1977. Probability Theory I. Graduate Texts in Mathematics, II (3): 378–382.
   Google Scholar
• Luo, J., H. Qin, W. Wang, and J. Wang. 2021. A note on asymptotic distributions in a network model with degree heterogeneity and homophily. Communications in Statistics - Theory and Methods 50 (21):5022–33. doi:10.1080/03610926.2019.1645852.
   Web of Science ®Google Scholar
• Luo, J., H. Qin, and Z. Wang. 2020. Asymptotic distribution in directed finite weighted random graphs with an increasing bi-degree sequence. Acta Mathematica Scientia 40 (2):355–68. doi:10.1007/s10473-020-0204-8.
   Web of Science ®Google Scholar
• Nepusz, T., H. Yu, and A. Paccanaro. 2012. Detecting overlapping protein complexes in protein-protein interaction networks. Nature Methods 9 (5):471–2. doi:10.1038/nmeth.1938.
   PubMed Web of Science ®Google Scholar
• Robins, G., P. Pattison, Y. Kalish, and D. Lusher. 2007. An introduction to exponential random graph (p*) models for social networks. Social Networks 29 (2):173–91. doi:10.1016/j.socnet.2006.08.002.
   Web of Science ®Google Scholar
• Stein, S., and C. Leng. 2020. A sparse β-model with covariates for networks. arXiv Preprint arXiv:2010.13604.
   Google Scholar
• Su, L., X. Qian, and T. Yan. 2018. A note on a network model with degree heterogeneity and homophily. Statistics & Probability Letters 138:27–30. doi:10.1016/j.spl.2018.02.046.
   Web of Science ®Google Scholar
• Von Mering, C., R. Krause, B. Snel, M. Cornell, S. G. Oliver, S. Fields, and P. Bork. 2002. Comparative assessment of large-scale data sets of protein-protein interactions. Nature 417 (6887):399–403. doi:10.1038/nature750.
   PubMed Web of Science ®Google Scholar
• Yan, T. 2015. A note on asymptotic distributions in maximum entropy models for networks. Statistics & Probability Letters 98:1–5. doi:10.1016/j.spl.2014.12.003.
   Web of Science ®Google Scholar
• Yan, T. 2021. Directed networks with a differentially private bi-degree sequence. Statistica Sinica doi:10.5705/ss.202019.0215.
   Web of Science ®Google Scholar
• Yan, T., B. Jiang, S. E. Fienberg, and C. Leng. 2019. Statistical inference in a directed network model with covariates. Journal of the American Statistical Association 114 (526):857–68. doi:10.1080/01621459.2018.1448829.
   Web of Science ®Google Scholar
• Yan, T., C. Leng, and J. Zhu. 2016. Asymptotics in directed exponential random graph models with an increasing bi-degree sequence. The Annals of Statistics 44 (1):31–57. doi:10.1214/15-AOS1343.
   Web of Science ®Google Scholar
• Yan, T., and J. Xu. 2013. A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices. Biometrika 100 (2):519–24. doi:10.1093/biomet/ass084.
   Web of Science ®Google Scholar
• Yan, T., Y. Zhao, and H. Qin. 2015. Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters. Journal of Multivariate Analysis 133:61–76. doi:10.1016/j.jmva.2014.08.013.
   Web of Science ®Google Scholar