# Advanced Topics in Financial Economics: Networks

### Inhalt

This course is intended for Master, Diploma or PhD students in the specialization ``Financial Economics''. No prior knowledge of network science is required. We make use of some matrix algebra and multivariate statistics. The course aims to give a wide overview over the techniques used in network science today. We start with the introduction of the common notation and techniques to represent networks. Further we will learn how to use quantitative measures of microscopic and macroscopic network properties. These topics typically feature some multidisciplinary aspects as they stem from Statistical Physics, Mathematics or Computer sciences. In the empirical part we focus on studies of networks from economics and finance before we end with networks from the natural sciences. Syllabus (preliminary): 1. Heritage of Network Science [F,WF1] Moreno and quantitative Sociology White and the Harvard revolution Six degrees Scale free networks and the world wide web 2. Games and Decisions on Networks [W,J9] Some special fixed networks Cooperation and coordination Strategic link formation 3. Mathematics of Networks [N6] Networks and their representation Weighted and directed networks Hypergraphs Bipartite networks Planar networks Degree, paths, components 4. Measures for Networks [N7] Centrality Closeness Betweenness Transitivity and reciprocity Structural balance Similarity, homophily and assortative mixing 5. Macroscopic Structure [N8] Components Shortest paths and small worlds Degree distributions and Power laws Clustering 6. Algorithms for Network Analysis [N(III),R,RB]2 Adjacency matrix and adjacency lists Clustering Shortest path Leading eigenvectors and eigenvector centrality Graph partitioning Block models Modularity Maximization The Map Equation 7. Random Graphs [N(IV)] Mean number of edges and degree Clustering Giant and small component Problems 8. Network Formation [N14,15] Preferential attachment Barbasi/Albert model Exponential random graphs other 9. Epidemics and Cascades [N17,J] Disease spreading Bass model SI/SIR/SIS/SIRS model Cascade models 10. Empirical Networks in Economics and Finance [J10,div] Social networks Supply chains Labor markets Trade networks Firm networks Financial contagion Interbank networks 11. Empirical Networks in other Disciplines [N(I),div] Technological networks Networks of information Biological networks

### Organisatorisches

Die angegebenen Prüfungszeiten beinhalten die Ausgabe und das Einsammeln der Prüfungsunterlagen. Die tatsächliche Prüfungszeit beträgt eine Stunde. Stated exam periods include distribution and collection of exam materials. Actual test duration is one hour.

### Literatur

basics: [N] Newman, M.E.J., Networks, An Introduction, Oxford, 2010. [J] Jackson, M.O., Social and Economic Networks, Princeton UP, 2008. further: [W F] Wasserman, S. and K. Faust, Social Network Analysis, Methods and Application, 1994. [W] Wilhite, A., Economic Activity on fixed Networks, in: Games on Networks, in Handbook of Computational Economics, Volume 2. Edited by L. Tesfatsion and K.L. Judd, 2006. [RB] Rosvall, M. and C. Bergstrom, Maps of random walks on complex networks reveal community structure. PNAS, 105(4):11181123, 2008. [F] Freeman, L, The Development of Social Network Analysis. Empirical Press, Vancouver, 2004. [R] Reichardt, J., Structure in Complex Networks, Lect. Notes Phys. 766, Springer, Berlin, 2009. Also have a look at Lázló Barabásis site, from which we might occasionally borrow a few slides: http://barabasilab.com/networksciencebook