Materials for Math 581.05 Computational Tools for Complex Networks (Fall 2020)

This course will introduce tools and methodology for analyzing complex social systems with network models. The first half of the course will cover standard network constructions and associated centrality metrics, clustering algorithms, dynamical models, and null models through classic papers and examples from the field. The second half of the course will focus on the discrete formulation of political redistricting problems and related applications of sampling connected graph partitions. In addition to the theoretical components, this course will provide resources and experiences for relevant software packages including networkx and gerrychain.

Weekly Topics

1. Introduction to NetworkX and Overview
2. Measures and Metrics
3. Null Models
4. Dynamics 1 (Diffusion)
5. Dynamics 2 (Compartment Models)
6. Clustering Methods 1 (Spectral Methods)
7. Clustering Methods 2 (Kitchen Sink)
8. Multiplex Networks
9. Applied Examples (Social Networks)
10. Introduction to Computational Redistricting
11. Geospatial Data
12. MCMC and Ensembles
13. Graph Partitioning
14. Applied Examples (Gerrymandering)
15. Applied Examples (Reform)

ReCom Ensemble	Boundary Ensemble