CS194-198 Networks: Models, Processes & Algorithms - Spring 2026
CLASS: Tue & Thu, 9:30AM - 11:00 AM, Soda 405
DISCUSSION: We, 17:00-18:00, Evans 70
INSTRUCTOR: Prof. Christian Borgs
GSI: Christian Ikeokwu
COURSE DESCRIPTION
We live in a world of networks: from our physical social network, to online
networks and the WWW, to the miscroscopic networks describing, e.g, pathways in
cancer cells, to name three examples. The goal of this class is to learn how
these networks work.
In particular, we will study several interrelated aspects of networks:
- Networks as structures
used to describe various interactions (from social interactions between people
to chemical interactions between proteins),
- Networks as the fabric on which various
economic, social and technological processes happen (from the spread of
(dis)information and epidemics to PageRank, which happens to be a probabilistic
process on the graph describing the WWW),
- Graph algorithms (algorithms to determine various
properties of networks).
The course is a new course, roughly at the
level of difficulty and mathematical abstraction as CS174, but obviously with a different thematic focus.
While there is
no book which covers exactly what I will cover here, most of the material can be
found in the book Networks, Crowds, and Markets: Reasoning About a Highly Connected World
by David Easley and Jon Kleinberg, albeit written in a less mathematical
language than I will use in my lectures. Courses I will be modelling mine
after are this and
this course at Cornell, and this course at
Caltech.
Prerequisites:
CS70 and either CS170 or EECS126, reflecting the required strong mathematical background / good level of mathematical maturity. In paticular, most of the homework and the final will be proof based.
List of Topics
- Graphs and Probability: Review of some concepts from probability,
review/introduction of basic concepts from graph theory
- Stucture: What are the structurual properties of common networks (power-law,
small world, etc)
- Network Models: Models for networks with these structural properties
(from random graphs to preferential attachment)
- Processes on Networks: Information cascades, epidemics, random walks, page
rank
- Graph Algorithms: Min-Cut/Max Flow, PageRank, determining influential nodes,
clustering
- Estimation: How to estimate network models from data, relation to
privacy
ATTENDANCE, ASSIGNMENTS, ETC.:
- The course will be in person and not be recorded, and I hope for
active participation of everyone enrolled. Therefore attendance is
mandatory.
- I will give weekly problem assignments, for which I encourage collaboration of 2-3 students,
but expect separately written up solutions from every participant.
- There will be a final, and probably also a midterm.
TENTATIVE SYLLABUS
- Network basics, properites of observed networks (Lecture 1)
- Review of probability theory (Lectures 2-3)
- Branching Process (Lecture 4)
- Thresholds in Random Graphs (Lectures 5-6)
- Giant Component in Random Graphs (Lectures 7-8)
- Random Graphs are small worlds (Lecture 9)
- Powerlaws 1: Configuration Model (Lectures 10-11)
- Powerlaws 2: Preferential Attachment (Lecture 12)
- Local and global communites (Lecture 13)
- Bow-tie structure for oriented graphs (Lecture 14)
- SIR Model 1: Homogeneous mixing (Lectures 15-16)
- SIR Model 2: Network effects (Lectures 17-18)
- PageRank and random walks (Lectures 19-20)
- Mixing, conductance, and spectral clustering (Lectures 21-22)
- Information cascades (Lecture 23)
- Recommendation systems (Lecture 24)
- Estimation of an underlying network model - Graphons (Lecture 25)
- Differential Privacy (Lecture 26)
- TBD (Lecture 27)
- Summary (Lecture 28)