Networks, Crowds and Markets - Fall 2025
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This course offers an introduction to the mathematics of networks, their dynamics, and their applications in economics and the social sciences. We combine rigorous probabilistic models with real-world data and case studies, moving from the basics of Erdős–Rényi random graphs to power laws, small-world phenomena, clustering, and preferential attachment. |
Announcements:
- The proposed project topics are released. To suggest your own topics contact me ASAP.
- The following problem set contains exercises covering most of the course. We will use it for the seminars.
- update: The midterm is scheduled for Monday, November 3, during the lecture.
- I added the proof sketches for both theorems of Lecture 2. The slides have been updated.
- The first lecture is on September 29, 3-4:30pm, in room 40.063.
Instructor:
| Prof | Piotr Zwiernik |
|---|---|
| piotr.zwiernik@upf.edu | |
| Office hours | Tuesday 2-3pm (20.202) |
Time & Location:
Lectures: Monday 3-4:30pm (40.063) and Tuesday 3-4:30pm (40.063).
Tutorials (group 1): 3-4:30pm (20.101) Tutorials (group 2): 4:30-6pm (20.101)
There are six tutorial sessions, in weeks: 3,4,5,6,7,8.
Suggested Reading
The following books complement the material presented in the lecture.
- (EK) Easley, Kleinberg (2010). Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press. Available online
- (B) Barabási (2016). Network Science. Cambridge University Press. Available online
- (N) Newman (2010). Networks: An Introduction. Oxford University Press.
- (MFD) Menczer, Fortunato, David (2020). A First Course in Network Science. Cambridge University Press. Available online
- (SK) Saoub (2017). A Tour Through Graph Theory. Springer.
Lectures and timeline (tentative)
| Week | Topic | Slides | Tutorials | Colabs | Lectures date | Timeline | |
|---|---|---|---|---|---|---|---|
| 1 | Motivation and first examples. Special graphs, degree. |
slides1 slides2 |
- | colab1 | 29/30 Sept | ||
| 2 | Degree distribution, graph isomorphism, adjacency matrix. Distance in graphs, diameter. Centrality measures. |
slides3 slides4 |
- | colab2 degree |
6/7 Oct | report topics published | |
| 3 | Centrality measures (continued), Linear algebra, Random walks. |
slides5 slides6 |
sem1 | 13/14 Oct | |||
| 4 | Pagerank algorithm and HITS, Erdös–Rényi model Degree distribution, threshold phenomena, clustering. |
slides7 slides8 |
colab3 | 20/21 Oct | |||
| 5 | Other random graph models, preferential attachment. | slides9 slides10 |
27/28 Oct | ||||
| 6 | midterm Small world, latent space random graphs. |
slides12 |
3/4 Nov | midterm | |||
| 7 | Power laws and hubs. Average path length, models with flexible degree distributions. Communities: definition and identification. Stochastic Block Model. |
slides13 slides14 |
10/11 Nov | deadline reports presentations 1 |
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| 8 | Social networks, forming mechanism. Matching markets |
slides15 slides16 |
17/18 Nov | presentations 2 | |||
| 9 | Spreading phenomena | slides17 slides18 |
- | 24/25 Nov | |||
| 10 | slides19 slides20 |
- | 1/2 Dec |
NetworkX guidelines
Although coding is not an essential part of this course, it is a very important complementary part. As the absolute minimum, you should try to run the code provided in class.
We use Python and NetworkX. Useful documentation and examples can be found on the GitHub of MFD book.
I suggest to start like that:
- Create a Google Colab account (you should be able to do it using your UPF account).
- Take a look at MFD:Appendix A. No need to read it completely. Use it as a reference.
- Start with the first colab.
Report topics taken:
Seminar 101:
- Friendship paradox
- Misinformation and Influence Dynamics on Social Media
- Learning in Networks: Diffusion of Information
Seminar 102:
- Cascading Failures and Systemic Risk
- Friendship paradox
- Structural Balance of social network
- Misinformation and Influence Dynamics on Social Media