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 recovery exam is scheduled 24 January, 9-11am, 40.063.
- If you want to see your exam, come on Monday, 22 Dec, to my office 20.202.
- Perhaps you will find it useful: mock test and last year’s exam. Note: This is not my exam and I included it only to give you more exercises to practice (there is a significant overlap with the material I discussed in class). This is not representative for the Thursday exam. I discusses the form of the exam in detail in the last lecture so follow these guidelines.
- For basic matrix algebra review check Section 1.4 and accompanying exercises here. I also recommend taking the course “Linear Algebra and Dynamical Systems”.
- The midterm with answers can be found here.
- In the bottom of the website you can see the dates for project presentations.
- Deadline for project submissions: November 18. Presentations start on November 19 and continue on November 24.
- 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 exam covers the material presented in the lecture and the accompanying slides as well as the problems discussed in the tutorial sessions. The following books complement what is 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 |
sem2 | colab3 | 20/21 Oct | ||
| 5 | Clustering and small world Power laws and hubs. |
slides9 slides10 |
sem3 | 27/28 Oct | |||
| 6 | midterm Static random graph models. |
extra slides12 |
sem4 | 3/4 Nov | midterm | ||
| 7 | Static random graph models. Communities: definition and identification. |
slides13 slides14 |
sem5 colabsem5 |
colab4 | 10/11 Nov | ||
| 8 | Social networks, forming mechanism. Matching markets |
slides15 slides16 |
17/18 Nov | deadline reports presentations 1 |
|||
| 9 | Spreading phenomena presentations |
slides17 - |
- | colab5 | 24/25 Nov | presentations 2 | |
| 10 | Spreading phenomena Summary |
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 presentations (15min+ques):
Group letters refer to the grouping from Aula Global.
101 (19 Nov)
- Group P: Friendship paradox
- Group B: Misinformation and Influence Dynamics on Social Media
- Group N: Cascading Failures and Systemic Risk
- Group H: Structural Balance of Social Networks
- Group G: Learning in Networks: Diffusion of Information
102 (19 Nov)
- Group C: Friendship paradox
- Group K: Misinformation and Influence Dynamics on Social Media
- Group F: Cascading Failures and Systemic Risk
- Group M: Structural Balance of social network
Lecture (25 Nov)
- Group D: Voting
- Group I: Percolation and Network Resilience
- Group E: Credit default prediction
- Group J: Kidney Exchange Project