# Seminar on Network Science

## Introduction

Complex networks from the Internet to various (online) social networks have a huge impact on our lives and it is thus an important research challenge to understand these networks and the forces that shape them. The emergence of the Internet has kindled the interdisciplinary field of Network Science, which is devoted to analyzing and understanding real-world networks.

Extensive research on real-world networks from many different domains like communication networks, social networks, protein-protein interaction networks, neural networks, etc. has revealed that many of these networks are similar in the sense that they share basic properties.

A typical example having all basic properties is the depicted snapshot of the AS-level graph of the Internet. Every node is an autonomous system and links exist if the corresponding ASs have a peering agreement for routing data between their respective sub-networks. The data was obtained from the Stanford Large Network Data Collection.

The depicted network has the so-called small-world property, i.e. it has a small diameter and small average distances. The degree distribution of the nodes follows a power-law, i.e. nodes' degrees are heterogeneous and there are many nodes with small degree and a few nodes with very high degree. (The size of the nodes in the network is depicted proportional to their degree.) Moreover, the network has high clustering, i.e. it has an abundance of small cliques and triangles.

The goal of this seminar is to introduce and explore the exciting field of Network Science. We will discuss the core properties of real-world networks and possible scientific explanations, i.e. generative models, of them. We will study broad range of models ranging from purely random graphs to game-theoretic approaches. Along the way we will also discuss some standard tools for analyzing real-world networks.

## Prerequisites

The seminar has no strict prerequisites. However, it is helpful to be somewhat fluent in Graph Theory and Mathematics in general.

## Seminar Mode

The seminar will be held in English. The exact mode of the seminar depends on the number of participants and will be determined in the first seminar session. Participants are expected to give an informative and interactive talk and to prepare a short write-up summarizing their talk.

## Grading

The grade will depend on the qualitiy of the seminar talk and the corresponding write-up.

## Dates

The first session of the seminar, where we introduce the topics and distribute the talks to students, will be held on Wednesday 11 April.

The seminar will be held weekly every Wednesday from 13:30 to 15:00 in room A-2.2.