363-0588-00L  Complex Networks

Semester Spring Semester 2015
Lecturers F. Schweitzer, I. Scholtes
Periodicity yearly course
Language of instruction English


Abstract The course provides an overview of the methods and abstractions used in (i) the quantitative study of complex networks, (ii) empirical network analysis, (iii) the study of dynamical processes in networked systems, (iv) the analysis of systemic risk in networked systems, (v) the study of network evolution, and (vi) data mining techniques for networked data sets.
Objective * the network approach to complex systems, where actors are represented as nodes and interactions are represented as links
* learn about structural properties of classes of networks
* learn about feedback mechanism in the formation of networks
* understand systemic risk as emergent property in networked systems
* learn about statistical inference techniques for data on networked systems
* learn methods and abstractions used in the growing literature on complex networks
Content Networks matter! This holds for social and economic systems, for technical infrastructures as well as for information systems. Increasingly, these networked systems are outside the control of a centralized authority but rather evolve in a distributed and self-organized way. How can we understand their evolution and what are the local processes that shape their global features? How does their topology influence dynamical processes like diffusion? And how can we characterize the importance and/or role of specific nodes? This course provides a systematic answer to such questions, by developing methods and tools which can be applied to networks in diverse areas like infrastructure, communication, information systems or (online) social networks. In a network approach, agents in such systems (like e.g. humans, computers, documents, power plants, biological or financial entities) are represented as nodes, whereas their interactions are represented as links.

The first part of the course, "Introduction to networks: basic and advanced metrics", describes how networks can be represented mathematically and how the properties of their link structures can be quantified empirically.

In a second part "Stochastic Models of Complex Networks" we address how analytical statements about crucial properties like connectedness or robustness can be made based on simple macroscopic stochastic models without knowing the details of a topology.

In the third part we address "Dynamical processes on complex networks". We show how a simple model for a random walk in networks can give insights into the authority of nodes, the efficiency of diffusion processes as well as the existence of community structures.

A fourth part "Statistical Physics of Networks: Optimisation and Inference" introduces models for the emergence of complex topological features which are due to stochastic optimization processes, as well as algorithmic approaches to automatically infer knowledge about structures and patterns from network data sets.

In a fifth part, we address "Network Dynamics", introducing models for the emergence of complex features that are due to (i) feedback phenomena in simple network growth processes or (iii) order correlations in systems with highly dynamic links.

A final part studies "Multiple roles of nodes and links", introducing recent research on automated role discovery in networks, as well as models for networks with multiple layers.
Lecture notes The lecture slides are provided as handouts - including notes and literature sources - to registered students only.
All material is to be found on Moodle at the following URL: https://moodle-app2.let.ethz.ch/course/view.php?id=1130
Literature See handouts. Specific literature is provided for download - for registered students, only.
Prerequisites / Notice There are no pre-requisites for this course. Self-study tasks (to be solved analytically and by means of computer simulations) are provided as home. Weekly exercises (45 min) are used to discuss selected solutions. Active participation in the exercises is strongly suggested for a successful completion of the final exam.