363-0588-00L Complex Networks
|jährlich wiederkehrende Veranstaltung
|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 robustness of networked systems, (v) the study of network evolution, and (vi) data mining techniques for networked data sets.
|* 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
* learn about statistical inference and data mining techniques for data on networked systems
* learn methods and abstractions used in the growing literature on complex networks
|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 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, biology 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 "Network Optimisation and Inference" introduces models for the emergence of complex topological features which are due to stochastic optimization processes, as well as statistical methods to detect patterns in large data sets on networks.
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 "Research Trends" introduces recent research on the application of data mining and machine learning techniques to relational data.
|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: Link
|See handouts. Specific literature is provided for download - for registered students, only.
|Voraussetzungen / Besonderes
|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 work. 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.