Networks Qualification Exam January 2015 Basic constructions: (un)directed (un)weighted networks, multiplex networks, bipartite graphs, hypergraphs Taxonomies: world network, scale free networks, trees, etc. Network statistics: degree, weighted degrees, degree distributions, power laws paths and geodesics in networks, connectivity assortativity and preferential attachment centrality: betweeness, eigenvector, Katz, etc. fragility and robustness: targeted vs. random attacks, relation to taxonomies Null models Erdos-Renyi networks, Barabasi-Albert networks, etc. Use of null models for parameter estimation Use of null models for computing significance Dimension Reduction multidimensional scaling principle components analysis Dynamics on networks Markov processes Diffusion Epidemic/disease models Clustering and partitions Linkage k-means spectral clustering modularity Sources: Newman’s Networks; Leibon, Pauls, and Rockmore’s Mathematical methods for complex systems (draft); Easley and Klineberg Part 1, Chapters 1-4 and Parts 5 and 6 ();
Networks Qualification Exam January 2015 Basic constructions: (un)directed (un)weighted networks, multiplex networks, bipartite graphs, hypergraphs Taxonomies: world network, scale free networks, trees, etc. Network statistics: degree, weighted degrees, degree distributions, power laws paths and geodesics in networks, connectivity assortativity and preferential attachment centrality: betweeness, eigenvector, Katz, etc. fragility and robustness: targeted vs. random attacks, relation to taxonomies Null models Erdos-Renyi networks, Barabasi-Albert networks, etc. Use of null models for parameter estimation Use of null models for computing significance Dimension Reduction multidimensional scaling principle components analysis Dynamics on networks Markov processes Diffusion Epidemic/disease models Clustering and partitions Linkage k-means spectral clustering modularity Sources: Newman’s Networks; Leibon, Pauls, and Rockmore’s Mathematical methods for complex systems (draft); Easley and Klineberg Part 1, Chapters 1-4 and Parts 5 and 6 ();
Networks_Syllabus.docx