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## November 22, 2013

### Network Analysis and Modeling (CSCI 5352)

This semester I developed and taught a new graduate-level course on network science, titled Network Analysis and Modeling (listed as CSCI 5352 here at Colorado). As usual, I lectured from my own set of notes, which total more than 150 pages of material. The class was aimed at graduate students, so the pace was relatively fast and I assumed they could write code, understood basic college-level math, and knew basic graph algorithms. I did not assume they had any familiarity with networks.

To some degree, the course followed Mark Newman's excellent textbook *Networks: An Introduction*, but I took a more data-centric perspective and covered a number of additional topics. A complete listing of the lecture notes are below, with links to the PDFs.

I also developed six problem sets, which, happily, the students tell me where challenging. Many of the problems were also drawn from Newman's textbook, although often with tweaks to make the more suitable for this particular class. It was a fun class to teach, and overall I'm happy with how it went. The students were enthusiastic throughout the semester and engaged well with the material. I'm looking forward to teaching it again next year, and using that time to work out some of the kinks and add several important topics I didn't cover this time.

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Lecture 1,2 : An introduction and overview, including representing network data, terminology, types of networks (pdf)

Lecture 3 : Structurally "important" vertices, degree-based centralities, including several flavors of eigenvector centrality (pdf)

Lecture 4 : Geometric centralities, including closeness, harmonic and betweenness centrality (pdf)

Lecture 5 : Assortative mixing of vertex attributes, transitivity and clustering coefficients, and reciprocity (pdf)

Lecture 6 : Degree distributions, and power-law distributions in particular (pdf)

Lecture 7 : Degree distributions, and fitting models, like the power law, to data via maximum likelihood (pdf)

Lecture 8 : How social networks differ from biological and technological networks, small worlds and short paths (pdf)

Lecture 9 : Navigability in networks (discoverable short paths) and link-length distributions (pdf)

Lecture 10 : Probabilistic models of networks and the Erdos-Renyi random graph model in particular (pdf)

Lecture 11 : Random graphs with arbitrary degree distributions (the configuration model), their properties and construction (pdf)

Lecture 12 : Configuration model properties and its use as a null model in network analysis (pdf)

Lecture 13 : The preferential attachment mechanism in growing networks and Price's model of citation networks (pdf)

Lecture 14 : Vertex copying models (e.g., for biological networks) and their relation to Price's model (pdf)

Lecture 15 : Large-scale patterns in networks, community structure, and modularity maximization to find them (pdf)

Lecture 16 : Generative models of networks and the stochastic block model in particular (pdf)

Lecture 17 : Network inference and fitting the stochastic block model to data (pdf)

Lecture 18 : Using Markov chain Monte Carlo (MCMC) in network inference, and sampling models versus optimizing them (pdf)

Lecture 19 : Hierarchical block models, generating structurally similar networks, and predicting missing links (pdf)

Lecture 20 : Adding time to network analysis, illustrated via a dynamic proximity network (pdf)

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Problem set 1 : Checking the basics and a few centrality calculations (pdf)

Problem set 2 : Assortativity, degree distributions, more centralities (pdf)

Problem set 3 : Properties and variations of random graphs, and a problem with thresholds (pdf)

Problem set 4 : Using the configuration model, and edge-swapping for randomization (pdf)

Problem set 5 : Growing networks through preferential or uniform attachment, and maximizing modularity (pdf)

Problem set 6 : Free and constrained inference with the stochastic block model (pdf)

posted November 22, 2013 11:00 PM in Teaching | permalink | Comments (1)