introduction_to_complex_networks [PIBBS]

Course Outline

Introduction (George)
- Preview of course, review of syllabus
- History
- Basics of graph theory
Random graphs (Wenyun):Introduce random graphs model, properties of random graphs and its applications. Readings:
- The Evolution of Random Graphs (Béla Bollobás, 1984)(recommended)
- Random graphs with arbitrary degree distributions and their applications(Newman, Strogatz & Watts, 2001) (required)
Small world networks (Wenyun): Introduce small world networks, properties of small world networks and their applications.Readings:
- Collective dynamics of small world networks (Watts & Strogatz, 1998)(required)
- Small worlds: How and why (Mathias & Gophal, 2001)(required)
- This may be useful, either in preparing the lecture, or as a reading: Schnettler 2009 A structured overview of 50 years of small-world research (PH)
- This should be a good review too: Newman (2000) Models of the small world. J. Stat. Phys 101 819-841. (PH)
Scale free networks (George)
- Error and attack tolerance of complex networks (Reka et al., 2000)
Measurements (Paul)
- The structure and function of complex networks (Newman, 2003)
Community structure (Paul)
- Detecting community structure in networks (Newman, 2004)
- Uncovering the overlapping community structure of complex networks in nature and society (Palla et al. 2005)
Software (Paul)
- UCINET 6 Software for Social Network Analysis
- Assignment: Use UCINET to perform a set of analyses (TBA) on real network data. We will provide around 3 sample datasets, or students may use any network dataset they find or create.
Fractals and fractality in networks (George)
- Self-similarity of complex networks (Song et al., 2005)
Scaling in networks (Wenyun): Introduce the scaling properties of different networks, similar scaling relation across systems. Readings:
Spatial networks (George)
Evolution of networks and/or network dynamics?
- Review: Dorogovtsev and Mendes (2002) Evolution of Networks. Advances in Physics 51, 1078-1187. They also expanded this into a book.
Final group project: choice of application of network theory/analysis or review paper (1-5 people, <5-page write-up. presentation)
Case studies (to be interspersed with theoretical readings above, and/or alloted their own class periods)
- Food webs
- Universal scaling relations in food webs (Garlaschelli,Caldarelli & Pietronero, 2003)
- Animal social networks
  - Social structure in a colonial mammal: Unraveling hidden structural layers and their foundations by network analysis (Wolf et al. 2007)
  - BOOK: Croft & James (2009) Exploring Animal Social Networks
- Human social networks
  - Network analysis in the social sciences (Borgatti et al. 2009)
  - Quantifying social group evolution (Palla, Barabási & Vicsek 2007)
  - BOOK: John Scott (1991, updated in 2000) Social Network Analysis: A Handbook.
  - BOOK: Wasserman & Faust (1994) Social Network Analysis: Methods and Applications.
  - BOOK: Knoke & Yang (2007) Social Network Analysis (1st released in 1982, thoroughly updated in 2007).
- Metabolic nets
- Neural networks
  - Generic aspects of complexity in brain imaging data and other biological systems (Bullmore et al. 2009)