This course discusses advanced topics from the field of network science. It builds on the topics that have been discussed in Web Science (706.716) course. Among other topics we will discuss the topics of network evolution and the connection between network structure and its function.

In recent years a new multidisciplinary research field called Network Science has emerged from various traditional fields such as
computer science, physics, social science, or information theory. Network Science revolves around the investigation of properties
of connections between individuals rather than on the investigation of individual properties. For example, the famous "Six Degrees of Separation"
phenomenon from social sciences can be only explained by the existence of specific structural properties of **
social networks.** Yet another example involves e.g. the success and growth of technologies such as the Internet or the Web.
This fastest growth of any technology in the human history can be explained by simple dynamic properties (e.g. preferential attachment)
of the **network representations** of the Internet and the Web.

In this course we will *investigate* and
*discuss* some of such advanced questions in modern networks. We will
mostly deal with *information networks.*

- Denis Helic (website)

Course topics include:

- Empirical analysis of networks
- Function and structure of complex networks
- Epidemics in complex networks
- Models of information diffusion

In this course the students will:

- Apply linear algebra to study networks
- Understand the relation between the function and the structure of complex networks
- Learn about the basic concepts of object diffusion via networks
- Understand models of disease, influence, or information diffusion

At the end of this course the students will know how to:

- To analyze a large network
- To interpret different network models
- To implement a simulation model
- To statistically infer various network properties

- 06.10.2017: Course organization / Mathematics of networks
- 13.10.2017: Mathematics of networks (cont.)
- 20.10.2017: Mathematics of networks (cont.)
- 27.10.2017: Measuring network properties
- 10.11.2017: Measuring network properties (cont.)
- 17.11.2017: Measuring network properties (cont.)
- 24.11.2017: Graph partitioning and community detection
- 01.12.2017: Graph partitioning and community detection (cont.)
- 15.12.2017: Graph partitioning and community detection (cont.)
- 12.01.2018: Function of Networks / Intro to Dynamical systems
- 19.01.2018: Epidemics
- 26.01.2018: Dynamical systems on networks
- 02.02.2018: Presentations of student projects

There will be 4 homework assignements in this lecture. Each assignment consists of 2 applied mathematics problems.

- Homework 1 (Tex File) 20.10.2017 (Homework 1 due 10.11.2017)
- Homework 2 (Tex File) 17.11.2017 (Homework 2 due 01.12.2017)

You (i) model a process taking place on a network, e.g. information spreading over Twitter, the flow of passengers in a traffic system, etc; (ii) detect communities in (a) large empirical network(s); (iii) empirically analyze (a) large empirical network(s); (iv) come up with your own idea. You decide on the methodology, e.g. by simulation, optimization, statistical inference, analytical, or a combined appraoch. For a desired network you perform experiments, obtain results and finally discuss the results.

Then, prepare 5 slides for the discussion:

- First slide: Introduction/Motivation
- Second slide: Methodology
- Third slide: Experimental setup
- Fourth slide: Results
- Fifth slide: Discussion

Send me the slides per e-mail as a PDF file until 01.02.2018 24:00. Subject of the e-mail must include [NetSci].

Projects and excercises will be discussed during lectures. We will try to find projects which are interesting and funny for both students and me ;-)

The total number of points that can be reached will be 80 (4x15 for homework + 20 for project).

There is a minimum number of points that you have to reach for both homework and project to pass the course:

- First two problem sheets: min. #points is 16
- Last two problem sheets: min. #points is 15
- Project: min. #points is 10

The grading scheme is as follows:

- 0-40 points: 5
- 41-50 points: 4
- 51-60 points: 3
- 61-70 points: 2
- 71-80 points: 1