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Synopsis for Networks


Number of lectures: 12 TT

Syllabus

  1. Introduction and Basic Concepts (1-2 lectures): nodes, edges, adjacencies, weighted networks, unweighted networks, degree and strength, degree distribution, other types of networks
  2. SmallWorlds (2 lectures): clustering coecients, paths and geodesic paths,Watts-Strogatz networks
  3. Toy Models of Network Formation (2 lectures): preferential attachment, generalizations of preferential attachment, network optimization
  4. Additional Summary Statistics and Other Useful Concepts (2 lectures): modularity and assortativity, degree-degree correlations, centrality measures, communicability, reciprocity and structural balance
  5. Random Graphs (2 lectures): Erdos-Renyi graphs, con guration model, random graphs with clustering, other models of random graphs or hypergraphs
  6. Community Structure (2 lectures): linkage clustering, optimization of modularity and other quality functions, overlapping communities, other methods and generalizations
  7. Dynamics on (and of) Networks (3-4 lectures): general ideas, models of biological and social contagions, percolation, voter and opinion models, temporal networks, other topics
  8. Additional Topics (0-2 lectures): games on networks, exponential random graphs, network inference, other topics of special interest to students

Reading List

  1. M. E. J. Newman (2010) Networks: An Introduction, Oxford University Press. [also, Newman's 2003 review article in SIAM Review for "older" topics]
  2. M. A. Porter (in preparation) A Terse Introduction to Networks, Springer.
  3. A. Barrat, M. Barthelemy and A. Vespignani (2008) Dynamical Processes on Complex Networks, Cambridge University Press.
  4. Various papers and review articles (e.g. Bocaletti et al, Physics Reports, 2006 as well as reviews on more speci c topics, such as Porter et al, Notices AMS, 2009 for community structure and Holme & Saramaki, arXiv paper, 2011 for temporal networks).

Last updated by Kathryn Gillow on Fri, 26/04/2013 - 3:00pm.
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