Networks are apparent in our daily lives. Typical examples of networks are: electrical and power networks, telephone or Internet data networks, traffic networks (highways, rail networks, airline service networks), manufacturing and distribution networks, or even social networks.


In this course, we are going to study two main aspects of networks:

1) Design of optimal network topologies. We will study two representative problems from this well-established research field using methods of complexity, algorithms and operations research.

2) Analysis of social networks. The growing public excitement by the global ``connectivity'' of the modern society has motivated scientists from multiple scientific disciplines (computer science, applied mathematics, economy and sociology) to develop this new interdisciplinary research field. We will study several graph-theoretical concept of social networks, their complexity and algorithmic approaches for their analysis.


Learning Objectives

This course should help graduate students to: a) understand information about networks, and b) develop models and algorithms to design, manage and analyse networks.

In particular the main aims of the course are to:
- provide the knowledge of the fundamental concepts of networks
- learn skills in modeling optimization or analysis tasks on networks
- learn skills in developing algorithmic techniques. This includes in particular the development of: 1) combinatorial algorithms (for polynomially solvable cases), 2) polynomial time heuristics with a constant approximation ratio and 3) exact algorithms applied to the corresponding mixed integer programming models.

1) Network design
- Two fundamental network design problems: Steiner trees and Steiner networks (aka survivable network design problems). Complexity, combinatorial algorithms with constant approximation ratio, block-cut trees, primal-dual algorithms, integer linear programming (ILP) models and branch-and-cut

2) Analysis of social networks
- Strong and week ties, betweenness measures, graph partitioning
- Networks in their surrounding contexts: homophily, affiliation
- Positive and negative relationships: structural balance, weaker form of structural balance, generalization
- Cascading behavior in networks: diffusion, cascades and clusters. Knowledge, threshold and collective action. The cascade capacity.
- Spreading epidemics in networks: branching process, SIR vs. SIS epidemic model. Analysis of branching process.

In the practical assignments, students will develop algorithms for solving related problems using standard network data sets available in the literature.

Total: 3 ECTS points (i.e, 75 hours):
25    hours: Lectures
10    hours: Student Presentations
20    hours: Preparing the programming exercise and homework assignments
19.0 hours: Preparing the written exam
  1.0 hours: Written Exam

Homeworks including programming exercises and oral exam