# Seminar - Advanced Topics in Network Science

## Brief Summary

This is a block seminar on a mixture of topics in network theory and analysis. We cover a broad set of topics, including in particular models for relational data and random graphs, as well as dynamical processes defined on networks, such as epidemic spreading dynamics.

## Organization

### Organizational Details

*Lecturer*: Michael Schaub

*Contact*: michael.schaub [at] rwth-aachen.de

*Time commitment*: 2 SWS with several deadlines spread throughout the lecture period. Block presentations at the end of the lecture period (or beginning of the lecture-free time)

*ECTS credits*: 4

*Study programs*: Master

*Language*: English

*Information regarding Corona etc.*: the seminar may be (partly or completely) virtual, depending on the latest advice.

### Seminar Structure

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

- In the mandatory introductory meeting (date tbc) all organizational details will be discussed; exact details will be announced via Email to participants in advance.
- Topics will be selected/assigned after the introductory meeting.
- Deadlines throughout the term will be discussed at the introductory meeting
- Final presentations will take place in a block seminar. The dates are not fixed yet, but will most likely be on one or two days at the end of the lecture-period or beginning of the lecture-free time.
- For more details see section “Seminar Details” below.

### Schedule of important dates

Introductory meeting: *Wednesday, September 2, 10:00-12:00 (tentative)*, exact details will be annouced to participants

Outline due: tbc

Initial paper due: tbc

Peer review due: tbc

Final paper due: tbc

Slides due: tbc

Presentations: tbc

### Selection Process

As seminar spots are in high-demand, please indicate clearly why you are interested in the seminar and how you and other students may benefit from your participation.

### Prerequisites

There are no formal prerequisites for this seminar, apart from a certain scientific and mathematical maturity. Depending on your preparation, some topics will be more accessible than others. Ideally, you will have some familiarity with graph theory, probability theory and dynamical systems, but this is not a must.

Lectures and seminars at RWTH that cover related topics include (not an exhaustive list): Kombinatorische Graphentheorie (Informatik 1), Theorie verteilter und paralleler Systeme (Informatik 1), Algorithmen für die Entdeckung von Communities in sozialen Netzwerken (Informatik 5), Machine Learning (Computer Vision), …

## Seminar Details

### Overview

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.

- Networks as relational data. In this context we are given a network (graph) 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/partitioning), as well as the study of random graph models etc.
- 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 (mis)information, opinion formation processes, or the spreading of viruses.

### Requirements

There are two main requirements for a successful attendance of the seminar

- you present your topic concisely in a 20-minute talk to the other seminar students
- you write a short paper on the topic, providing more detail than the talk

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.

### Topics

Possible topics will be discussed in the first meeting. As an indication, these could include A) random graph models such as stochastic block models, configuration models, or random dot product graphs, topics such as community detection, link prediction, or other data mining tasks. B) dynamical processes such as diffusion processes on graphs, opinion formation processes or epidemic spreading models.

### Paper

The papers will be written in conference style, using a provided LaTeX template (no word submissions are accepted). This means, 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 (2-3 reports) 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 reports submitted by other seminar attendees as well (on 2-3 papers).

Plagiarism of any form is of course unacceptable and will lead to your immediate suspension from the seminar.

### Talks

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. Ideally your talk should give the audience a good grasp of the topic you have been focussing on.

The talk format will be 20 minutes + 5-10 minutes for questions, answers and discussions.

### Material

How to write good papers – see the advice and links collected by John Tsitsiklis here:

https://www.mit.edu/~jnt/write.html

Some introductory books on Network Science

- Newman, Mark. Networks. Oxford university press, 2018
- Easley, David, and Jon Kleinberg. Networks, crowds, and markets. Vol. 8. Cambridge: Cambridge university press, 2010. (online version: https://www.cs.cornell.edu/home/kleinber/networks-book/)
- Kolaczyk, Eric D., and Gábor Csárdi. Statistical analysis of network data with R. Vol. 65. New York, NY: Springer, 2014.