# Scale-free networks

## Required readings

- R. Albert et al., Diameter of the world-wide web,
*Nature*, 1999 / B.A. Huberman and L.A. Adamic, Growth dynamics of the world-wide web, *Nature*, 1999. (in the same PDF)
- A.-L. Barabási and R. Albert, Emergence of scaling in random networks,
*Science*, 1999.
- M.E.J. Newman, Power laws, pareto distributinos and Zipf's law,
*Contemporary physics*, 2005 - A nice overview of power-law phenomena and mechanisms

## Recommended readings

- Barabasi, Ch. 3
- A. Clauset et al., Power-law distributions in empirical data,
*SIAM Review*, 2009.
- M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions,
*Internet Mathematics*, 2004.
- R. Cohen and S. Havlin, Scale-Free Networks Are Ultrasmall,
*PRL*, 2003.
- M.E.J. Newman et al., Random graphs with arbitrary degree distributions and their applications,
*PRE*, 2001

## Further readings

- A.-L. Barabási et al., Mean-field theory for scale-free random networks,
*Physica A*, 1999.
- R. Cohen and S. Havlin, Scale-Free Networks Are Ultrasmall,
*PRL*, 2003.
- M.E.J. Newman et al., Random graphs with arbitrary degree distributions and their applications,
*PRE*, 2001 - Another type of graph model.
- K.-I. Goh et al., Universal Behavior of Load Distribution in Scale-Free Networks,
*PRL*, 2001 - So-called 'static scale-free model.
- K. Klemm and V.M. Eguiluz, Highly clustered scale-free networks,
*PRE*, 2002 - You can add more clustering by limiting the 'memory' of nodes.
- P. Holme and B.J. Kim, Growing Scale-Free Networks with Tunable Clustering,
*PRE*, 2002 - Another way to achieve high clustering
- B.J. Kim et al., Path finding strategies in scale-free networks,
*PRE*, 2002.

## Questions

- What is power-law distribution?
- What's the difference between Zipf's law and power-law?
- What are the distributions that follow power-law?
- How to visualize an empirical power-law distribution?
- Why isn't linear regression in log-log scale the best way?
- What does 'scale-free' mean?
- What are the two main components of Barabási-Albert model?