During the last decade it has become clear that the topology in many systems, ranging from technological to social to biological, is not well described by regular lattices nor by random graphs. Complex networks, characterized by small-world effects, large connectivity fluctuations, clustering, correlations and other nontrivial features are often a better description of many natural and man-made systems. Since many of such networks describe the topological patterns that mediate various sorts of interactions among nodes, it is natural and interesting to wonder what is the effect of complex topologies on dynamical processes taking place on them.

a la Ginzburg for them. Other interesting issues are the applicability of Finite-Size-Scaling theory to processes on scale-free topologies and the problem of how to characterize dynamical correlations on network.

**People**: Claudio Castellano

**References**:

- C. Castellano and R. Pastor-Satorras

Non mean-field behavior of the contact process on scale-free networks

Phys. Rev. Lett.96, 038701 (2006). [cond-mat/0506605]

- C. Castellano and R. Pastor-Satorras

- Zero temperature Glauber dynamics on complex networks

J. Stat. Mech. P05001 (2006). [cond-mat/0602315]

- C. Castellano and R. Pastor-Satorras

Reply to the Comment on the paper "Non-mean-field behavior of the contact process on scale-free networks"

Phys. Rev. Lett.

98, 029802 (2007). [cond-mat/0701275]

- C. Castellano and R. Pastor-Satorras

- Routes to thermodynamic limit on scale-free networks

Phys. Rev. Lett.**100**, 148701 (2008). [arXiv:0710.2784]

- M. Boguna', C. Castellano and R. Pastor-Satorras

- Langevin approach for the dynamics of the contact process on annealed scale-free networks
- [arXiv:0810.3000]