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 and (v) the study of network evolution.
* 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 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 epidemic spreading, cascading failures or consensus? And how can you 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 or (online) social networks. In a network approach, agents in such systems (like e.g. humans, computers, documents, power plants or financial entities) are represented as nodes, whereas their interactions are represented as links.
The first part of the course, "Topology of Complex Networks", describes how networks can be represented mathematically and how the properties of their link structures can be quantified empirically. We further address how general statements about crucial properties like connectedness, robustness or efficiency can be made based on simple macroscopic stochastic models without knowing the details of a topology.
In the second 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 information diffusion processes as well as the existence of community structures. We further address the influence of the topology of complex networks on the spreading of epidemics and cascading failures as well as the emergence of synchronization and consensus.
In the third part "Network evolution" we introduce models for the emergence of complex topological features which are due to (i) stochastic optimization processes and heterogeneous node fitness, (ii) feedback phenomena in simple network growth processes or (iii) complex order correlations in systems with highly dynamic links.
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.
Performance assessment information (valid until the course unit is held again)