Schedule

Readings in normal font should be completed and annotated ahead of lecture.
Readings in italic provide optional additional depth on the material.

Reading sources:

MEJN: Networks: An Introduction by Newman (2018).
HZB+PSC: Network Science: Models, Mathematics, and Computation by Heather Zinn Brooks and Phil Chodrow.

Week 1

Mon Feb. 10	Welcome!
Mon Feb. 10	We introduce our topic and discuss how the course works.
	Learning Objectives Getting Oriented	Reading Course syllabus
Wed Feb. 12	Networks and Their Representations
Wed Feb. 12	We introduce several different types of connected systems and discuss ways of representing them in mathematical and computational structures.
	Learning Objectives Network Fundamentals	Reading Newman 6.1 - 6.6	Notes Networks and their Representations	Warmup Newman 6.2

Week 2

Mon Feb. 17	Degrees, Walks, and Paths
Mon Feb. 17	We study several important structural properties that can be computed from the adjacency matrix of a graph.
	Learning Objectives Network Fundamentals	Reading Newman 6.10 - 6.12	Notes Degrees, Walks, and Paths	Warmup Leading Eigenvalue of the Complete Graph
Wed Feb. 19	Connected Components and the Graph Laplacian
Wed Feb. 19	We study the connected components of a graph. We also relate the number of connected components to another important matrix representation of a graph, the graph Laplacian.
	Learning Objectives Network Fundamentals	Reading Newman 6.14	Notes Connected Components and the Graph Laplacian	Warmup Properties of the Graph Laplacian

Week 3

Mon Feb. 24	Network Centrality
Mon Feb. 24	Many networks define a concept of centrality, importance, or rank. We discuss several mathematical methods for operationalizing these ideas and computing them from network data.
	Learning Objectives Measuring Networks	Reading Newman 7.1.1-7.1.4	Notes Centrality	Warmup Leading Eigenvector of a Regular Graph
Wed Feb. 26	Network Visualization
Wed Feb. 26	We study an algorithm used to draw networks, and also discuss some of the limitations of visualization in large networks.
	Learning Objectives Measuring Networks	Reading Newman 6.14.2 (very short, please allocate some extra time for the warmup)	Notes Visualizing Networks (And Why You Shouldn't)	Warmup Gradient of a Visualization Objective

Week 4

Mon Mar. 03	Structure of Empirical Networks
Mon Mar. 03	We conduct a comparative study of several empirical networks.
	Learning Objectives Measuring Networks	Reading Newman, 10.1-10.4.1	Notes Structure of Empirical Networks	Warmup Triangle Counting, Revisited
Wed Mar. 05	Random Graphs: Erdős–Rényi
Wed Mar. 05	We begin our investigation of random graphs with the Erdős–Rényi model, the most random of graphs.
	Learning Objectives Random Graphs	Reading Newman, 11.1-11.4	Notes Random Graphs: Erdős–Rényi	Warmup Binomial Distribution

Week 5

Mon Mar. 10	Random Graphs: Erdős–Rényi II
Mon Mar. 10	We continue our study of the Erdős–Rényi model, with special focus on the structure of connected components.
	Learning Objectives Random Graphs	Reading Newman, 11.5	Notes Random Graphs: Erdős–Rényi	Warmup Triangles in Sparse ER

References

Newman, Mark E. J. 2018. Networks: An Introduction. Oxford University Press.