Deliverables - D04 Universality in Networks

In works done by three of the groups in the consortium we have analyzed the hierarchical structure of complex networks by looking at the formation of cycles of different orders. In publications below we have studied the properties of metrics aimed at the characterization of grid-like ordering in complex networks. These metrics are based on the global and local behaviour of cycles of order four which are the minimal structures able to identify rectangular clustering. The analysis of data from real networks reveals the ubiquitous presence of a high level of grid-like ordering that is non-trivially correlated with the local degree properties. These observations provide new insights on the hierarchical structure of complex networks. In a separate publication by the Swiss group the number of scaling of the number of loops as a function of the system size is investigated in particular analytical results are obtained for the Barabási-Albert scale-free model. Finally in another publication we relate the formation of social capital with the number of squares formed in the network. We study in detail the community of users of the PGP encryption system and show that this community creates social capital very effectively. The deliverable is formed by the publications

  1. Number of Loops of size h in growing scale-free networks.
    G. Bianconi and A.Capocci
    ArXiv:cond-mat/0212028 (2002).

  2. Epidemic spreading in correlated complex networks.
    M. Boguñá and R. Pastor-Satorras
    Physical Review E 66 047104 (2002).

  3. Introduction to Complex Networks.
    G. Caldarelli
    Proceedings of the 7th Conference on Statistical and Computational Physics Granada (2002).

  4. Cycles structure and local ordering in complex networks.
    G. Caldarelli, R. Pastor-Satorras and A. Vespignani
    ArXiv:cond-mat/0212026 (2002).

  5. Exploration bias of Complex Networks.
    P. De Los Rios
    Proceedings of the 7th Conference on Statistical and Computational Physics Granada (2002).

  6. Dynamical properties of model communication networks.
    R. Guimerà, A. Arenas, A. Díaz-Guilera and F. Giralt
    Physical Review E 66, 026704 (2002).

  7. Optimal network topologies for local search with congestion.
    R. Guimerà, A. Díaz-Guilera, F. Vega-Redondo, A. Cabrales, and A. Arenas
    Physical Review Letters 89, 248701 (2002).

  8. Critical load and congestion instabilities in scale-free networks.
    Y. Moreno, R. Pastor-Satorras A. Vázquez and A. Vespignani
    ArXiv:cond-mat/0209474 (2002).

  9. Epidemics and immunization in scale-free networks.
    R. Pastor-Satorras and A. Vespignani
    Handbook of Graphs and Networks: From the Genome to the Internet, eds. S. Bornholdt and H. G. Schuster, Wiley-VCH, Berlin, pp. 113-132 (2002).

  10. Topology and correlations in structured scale-free networks.
    A. Vázquez, M. Boguñá, Y. Moreno, R. Pastor-Satorras and A. Vespignani
    ArXiv:cond-mat/0209183 (2002).

  11. Size of Quantum Networks.
    G. Bianconi
    ArXiv:cond-mat/0301551.

  12. Absence of Epidemic threshold in scale-free networks with degree correlations.
    M. Boguñá R. Pastor-Satorras and A. Vespignani
    Physical Review Letters 90, 028701 (2003).

  13. Epidemic spreading in complex networks with degree correlations.
    M. Boguñá R. Pastor-Satorras and A. Vespignani
    ArXiv:cond-mat/0301149 to appear in Lecture notes in Physics (2003).

  14. Self-similar community structure in organizations
    R. Guimerà, L. Danon, A. Diaz-Guilera, A. Arenas
    preprint
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