Spring 2015 Syllabus Complex Networks Prof. Frank Schweitzer, Dr. Ingo Scholtes Chair of Systems Design, ETH Zurich sg-complex@ethz.ch Lecture: Tuesday, 10:15-11:55 (V), HG E 1.2 Exercise: Tuesday, 09:15-10:00 (U), HG G 26.1 Some exercises require analytical computations, others can be carried out with software such as python, igraph or R. Sample programs and code skeletons will be provided. During the exercise classes, students will present their solutions which will then be discussed. 1. Introduction to Networks: Basic and Advanced Metrics Lecture 01 Motivation 17.02.2015 Educational Objective: In this lecture, participants will get an overview of the course and will learn the dierences between an agent-based modeling and a complex networks perspective. Administrative issues and overview of the course Introduction: Agent-based modeling vs. a network approach Motivation: The role of network structures in complex systems Illustrative examples of complex networks in nature, society, economy and technology Exercise 01: Introduction to igraph and python due 24.02.2015 1/8
Lecture 02 Introduction to Networks 24.02.2015 Educational Objective: In this lecture, students will learn how to mathematically represent complex networks and how to quantitatively analyse the importance of nodes. Basic denitions: graph, network, adjacency matrix, path, cut, degree Importance of nodes: betweenness, closeness and degree centrality Modules and clusters: clustering coecient and modularity Example: Open Source collaboration network Exercise 02: Analysis of empirical networks with igraph due 03.03.2015 2. Stochastic Models of Complex Networks Lecture 03 Ensemble Perspective of Complex Networks 03.03.2015 Educational Objective: In this lecture, participants will learn how networks can be represented and analysed from a statistical point of view. Graph theory vs. network science: the ensemble perspective Erdös-Renyi (ER) random graph model Degree distribution and average degree in ER graphs Counterexample: degree distribution in OSS collaboration network Exercise 03: Exploring the connectivity phase transition in igraph due 10.03.2015 2/8
Lecture 04 Small-world networks 10.03.2015 Educational Objective: In this lecture, participants will learn how the distribution of node degrees inuences systemic risk in networked systems. Navigability and funneling Watts-Strogatz model Small-world networks Example: Scientic coauthorship network Exercise 04: Watts-Strogatz model in igraph and python due 17.03.2015 Lecture 05 Connectivity in Complex Networks 17.03.2015 Educational Objective: In this lecture, students will understand what kind of statements one can make about the properties of a network if one only knows the distribution of node degrees. Ensembles of networks with xed degree distribution: Molloy-Reed algorithm Mathematical analysis: generating functions The friendship paradox: Analytical explanation Condition for giant connected component: Molloy-Reed criterion Example: OSS collaboration network Exercise 05: Molloy-Reed algorithm with python and igraph due 24.03.2015 3/8
Lecture 06 Scale-Free Networks and Limitations of Ensemble Studies 24.03.2015 Educational Objective: In this lecture, participants will learn how heterogeneity of degrees inuences robustness and what fallacies one encounters when applying ndings from ensemble studies to real networks. Analysis of network robustness: random failures Scale-free networks Limitations of ensemble-based approaches (Counter-)example: AS-level Internet topology Exercise 06: Simulating random failures: Finite-size eects due 31.03.2015 3. Dynamical Processes on Complex Networks Lecture 07 Diusion in Complex Networks 31.03.2015 Educational Objective: In this lecture, students will learn how the structure of complex networks inuences the speed and dynamics of diusion processes. Random walk processes in complex networks Markov chain convergence theorem Diusion speed in complex networks Example: diusion speed in Watts-Strogatz networks Exercise 07: Simulating diusion with igraph and numpy due 14.04.2015 Easter break 07.04.2015 4/8
Lecture 08 Spectral Properties of Complex Networks 14.04.2015 Educational Objective: In this lecture, students will learn how the inuence of a network's topology on dynamical processes is captured in the eigenvalues of adjacency matrices and how we can use this to dene measures of node importance. Powers of adjacency matrices and algebraic methods Algebraic connectivity, Fiedler vector, eigenvalue gap and eigenratio of complex networks Feedback centralities: eigenvector centrality and PageRank Example: PageRank in a network of linked documents Exercise 08: Diusion in networks with community structures due 21.04.2015 4. Statistical Physics of Networks: Optimisation and Inference Lecture 09 Topology Optimisation in Equilibrium Networks 21.04.2015 Educational Objective: In this lecture, students will understand why statistical physicists are often studying complex networks and they will learn that the emergence of some network structures can be understood as a (distributed) optimisation process. Complex networks: the perspective of statistical mechanics Link costs and link potentials: generating energy landscapes for networks Heterogeneous agent tness: emergence of scale-free networks Example: Gene regulatory network of Escherichia Coli Exercise 09: The tness model in igraph and python due 28.04.2015 5/8
Lecture 10 Statistical Inference 28.04.2015 Educational Objective: In this lecture, students will learn how the ensemble perspective on complex networks can be used for the automated extraction of information from data sets on networked systems. Statistical ensembles and statistical inference Approaches to inference: Bayesian vs. maximum likelihood estimation Generative models of networks Example: stochastic block models Exercise 10: Community detection using stochastic block models due 05.05.2015 5. Network Dynamics Lecture 11 Structure formation in growing networks 05.05.2015 Educational Objective: In this lecture, students will learn that feedback phenomena in the growth of networks can lead to the formation of complex structures. A non-equilibrium perspective on growing complex networks Feedback in network growth: the preferential attachment model Analyzing preferential attachment: emergence of scale-free degree distributions Example: Modeling growing citation networks Exercise 11: Preferential attachment in igraph and python due 12.05.2015 6/8
Lecture 12 Temporal Networks 12.05.2015 Educational Objective: In this lecture, students will understand that the dynamics of links in networks adds an additional dimension of complexity on top of the network topology. Motivation: inseparable time-scales between network evolution and dynamical processes Basics of temporal networks: time-respecting paths, inter-event times and node activities Time-aggregated representations and non-markovian temporal networks Example: RealityMining dynamic social network Exercise 12: Betweenness centrality in temporal networks due 19.05.2015 6. Multiple roles of nodes and links Lecture 13 Role discovery in networks 19.05.2015 Educational Objective: In this lecture, participants will learn how network structures can be simplied by grouping nodes that have similar roles, and how these roles can be detected based on network data. Roles vs. nodes in complex networks Role discovery as an optimisation problem Non-negative matrix factorisation Example: Role discovery in in coauthorship networks Exercise 13: Role discovery in igraph and python due 26.05.2015 7/8
Lecture 14 Multi-layer networks 26.05.2015 Educational Objective: In this lecture, students will see that the coupling of dierent layers of complex networks can lead to new systemic properties. Socio-technical and cyber-physical systems: Multiple layers of complex networks Network formation: Coupling and feedback between network layers Network cascades in multi-layer networks Example: Collaboration and citation networks in science Exercise 14: Question and Answer Session Exam (Session) to be determined 8/8