(Advanced) Topics in Network Science

Networks have become a widely adopted paradigm to model a wide range of systems, cutting across science and engineering, ranging from biological systems to social networks and technical systems such as the Internet.

In this seminar you will be exposed to a broad range of topics related to network analysis and modeling, with a primary focus on two perspectives:

1. Networks as relational data. In this context we are given a network and would like to quantify and infer potential regularities, patterns, and various other network features, and assess whether these are consistent with statistical models we may have of our network data. This includes topics such as community detection, graph clustering or partitioning, as well as the study of random graph models etc.
2. Dynamical Systems on networks. In a range of applications we observe a dynamical process on a network and would like to understand if and how its behavior is influenced by the network structure. This includes topics such as the spread of information, opinion formation processes, or the spreading of viruses.

We will give an overview over possible seminar paper topics at the bottom of this page.

Requirements for Successful Participation

There are three main requirements for successful attendance of the seminar:

1. You present your topic concisely in a 12-minute talk to the other seminar students.
2. You write a short paper on the topic, providing more detail than the talk.
3. You successfully complete the milestones on the way, as outlined by moodle.

Furthermore, you are expected to engage in discussions about each talk and provide constructive feedback on earlier drafts of the reports by your fellow students.

Paper

The papers will be written in conference style, using a provided LaTeX template. This means that after you have found your topic, you will write your paper and submit it for “peer review” by the other seminar members. You will receive constructive feedback on how to improve the paper and then be able to submit an updated, final version which is the one that will be graded. Note that this implies that you will have to write some short reviews on the papers submitted by other seminar attendees as well.

Presentation

In contrast to the paper, the talk is not supposed to describe everything in full detail, but you should provide an overview on your topic, highlighting the important concepts and ideas.
It should then focus on a few of those ideas—those that were foundational to your paper—and explain them in more detail: this gives the audience something substantial to learn, and adds much value to your presentation. Remember to adjust the content and pace of your presentation to your target audience, which in this case is a group of your student peers.

The talk format will be 12 minutes + 3 minutes for questions, answers and discussions.

Organisation

Please account for the following points when planning your semester and/or holidays:

• In the mandatory introductory meeting, all organizational details will be discussed.
• Topics will be selected/assigned after the introductory meeting.
• Final presentations will take place in a block seminar.

Tentative Timetable

Throughout the semester, students have to write and present their seminar paper in several milestones as outlined below:

List of topics

Below, you can find a tentative list of topics that we regularly offer for our seminar.

The stochastic block model and its degree corrected variant

Change Point Detection

Node Embeddings

Graph Neural Networks

Community detection using spectral methods

Graph Signal Processing and Frequency Analysis

Topological Data Analysis and Persistent Homology

Basic Network Techniques for Single-Cell Data

Percolation as a model of network reliability

Synchronization phenomena in networks

Collective Action on Networks

Polarization in Social Networks

Evolutionary Games on Networks

Graph Signal Processing on Images

Graph Sparsification

Graph Coarsening: Another Graph Compression Strategy

From Eigenvalues to Power Spectra

Heuristics for Critical Node Problem

Random walks for community detection

Message passing on graphs

Graph Neural Networks Training

Sampling Theory on Graphs

Reconstructing Graph Signals

Optimal Transport on Graphs: Fused Gromov-Wasserstein

Dynamical Node Embeddings

Neuronal Dynamics and Spiking Neural Networks

Fitness Landscapes

Gene Regulatory Networks