# (Approximate) course outline

- Jan 12: Intro, why we do this
- Jan 17: Guest lecture by Katherine Heller, Duke Statistics
- Jan 19: Guest lecture by James Moody, Duke Sociology
- Jan 24: Graph theory and random graphs
- Jan 26: Graph theory and random graphs
- Jan 31: Graph attributes: centrality; Lab 1
- Feb 2: Small world networks
- Some additional reading: Bollobas Chapter 10.
- Bollobás, Belá. “The diameter of random graphs.” Transactions of the American Mathematical Society 267.1 (1981): 41-52.
- Watts, Duncan J., and Steven H. Strogatz. “Collective dynamics of ‘small-world’networks.” nature 393.6684 (1998): 440-442.

- Feb 7: Power law degree distributions
- Clauset, Aaron, Cosma Rohilla Shalizi, and Mark EJ Newman. “Power-law distributions in empirical data.” SIAM review 51.4 (2009): 661-703.
- Barabasi, Albert-Laszlo. Network Science, chapters 4 and 5.
- Lab 2: Blitzstein, Joseph, and Persi Diaconis. “A sequential importance sampling algorithm for generating random graphs with prescribed degrees.” Internet mathematics 6.4 (2011): 489-522.

- Feb 9: Exponential Random Graph Models (Intro and MLE)
- Feb 14: Exponential Random Graph Models (Bayes and failures)
- Feb 16: Bayesian ERGMs and Structural Equivalence
- Bayesian ERGM: Caimo and Frield 2011
- Structural Equivalence: Chapter 9 of Wasserman and Faust.

- Feb 21: Stochastic Equivalence and intro to stochastic blockmodels
- Feb 23: Stochastic blockmodels (MLE and Bayes)
- Holland, Paul W., Kathryn Blackmond Laskey, and Samuel Leinhardt. “Stochastic blockmodels: First steps.” Social networks 5, no. 2 (1983): 109-137.
- Snijders, Tom AB, and Krzysztof Nowicki. “Estimation and prediction for stochastic blockmodels for graphs with latent block structure.” Journal of classification 14, no. 1 (1997): 75-100.

- Feb 28: …
- March 2: Stochastic blockmodels and graphons (theory)
- Rohe, Karl, Sourav Chatterjee, and Bin Yu. “Spectral clustering and the high-dimensional stochastic blockmodel.” The Annals of Statistics (2011): 1878-1915.
- What is a graphon? by Daniel Glasscock
- Airoldi, Edo M., Thiago B. Costa, and Stanley H. Chan. “Stochastic blockmodel approximation of a graphon: Theory and consistent estimation.” In Advances in Neural Information Processing Systems, pp. 692-700. 2013.
- Chan, Stanley and Airoldi, Edo. “A CONSISTENT HISTOGRAM ESTIMATOR FOR EXCHANGEABLE GRAPH MODELS”.

- March 7: Exchangeability and Aldous-Hoover theorem
- Aldous, David. “Representations for partially exchangeable arrays of random variables”. Journal of Multivariate Analysis 11, no. 4 (1981): 581-598.

- March 9: (catch up)
- March 14: Spring Break
- March 16: Spring Break
- March 21: “Network regression” and other decompositions
- D Krackhardt (1988). ``Predicting with networks: Nonparametric multiple regression analysis of dyadic data.’’
- Butts (2008). ``Social network analysis with sna.’’

- March 23: Testing for independence
- Volfovsky and Hoff (2015). “Testing for nodal dependency in relational data matrices”
- Fosdick and Hoff (2015). “Testing and Modeling Dependencies Between a Network and Nodal Attributes”

- March 28: Latent Space Models (MLE)
- Hoff, Raftery and Handcock (2002). ``Latent space approaches to social network analysis’’. JASA
- Hoff (2005). ``Bilinear mixed effects models for dyadic data’’

- March 30: Bayesian approaches to latent space models
- Hoff (2007). ``Modeling homophily and stochastic equivalence in symmetric relational data’’

- April 4: Bayesian approaches to latent space models
- Hoff (2016). “Dyadic data analysis with amen”

- April 6: Fixed rank nomination schemes, etc.
- Hoff, Fosdick, Volfovsky and Stovel (2013). ``Likelihoods for fixed rank nomination networks’’ (Networy Science)

- April 11: Feasible covariance estimation
- April 13:
- April 18: Student presentations in class and in lab. Attendance required…