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

This term the course is fully online. Each Friday 10:00-11:00 there will be a Q&A session in WebEx. The meeting information:

Meeting link: | https://tugraz.webex.com/tugraz/j.php?MTID=m38c1052b26a1b17e1acc3d6b3a7b1e9d |

Meeting number: | 137 680 2842 |

Password: | i2UjAJQm39P |

Host key: | 544322 |

The weekend before a Q&A session I'll upload new videos and new lecture notes for you to watch. On Friday we can then shortly discuss all open questions from the last video.

- Course organization: (Video)
- Mathematics of networks: (Video: Part I, Part II, Part III, Part IV, Part V, Part VI, Part VII, Part VIII, Part IX, Part X)
- Measuring network properties: (Video: Part I, Part II, Part III, Part IV, Part V, Part VI, Part VII)
- Graph partitioning and community detection: (Video: Part I, Part II, Part III, Part IV, Part V)
- Function of Networks: (Video)
- Intro to Dynamical systems: (Video: Part I, Part II)
- Epidemics: (Video)
- Dynamical systems on networks: (Video)
- Solutions to selected problems:
- Quadratic form of graph Laplacian
- Diffusion on networks
- Hubs and authorities
- Random walks and graph Laplacian

- Project information:

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

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

For ideas, software and dataset repositories check these slides.

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