| Abstract: | Network science have been focused on the
properties of a single isolated network that does not interact or
depends on other networks. In reality, many real-networks, such as
power grid, protein networks, transportation and communication
infrastructures interact and depend on other networks. I will present a
framework for studying the vulnerability of networks of interdependent
networks. In interdependent networks, when nodes in one network fail, they
cause dependent nodes in other networks to also fail. This may happen
recursively and can lead to a cascade of
failures and to a sudden fragmentation of the system.
I will present analytical solutions for the critical threshold
and the giant component of a network of n interdependent networks.
I will show, that the general theory has many novel features
that are not present in the classical network theory. Our results for
network of n networks suggest that the classical percolation
theory extensively studied in physics and mathematics is a limiting
case of n=1 of the general theory of percolation in network of networks.
I will also show that interdependent networks embedded in space are
significantly more vulnerable compared to non embedded networks.
References:
[1] S. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin,
Nature, 465, 0893 (2010)
[2] R. Parshani, S. Buldyrev, S. Havlin, PRL, 105, 048701 (2010)
[3] R. Parshani, S.V. Buldyrev, S. Havlin, PNAS 108, 1007 (2011)
[4] J. Gao, S. Buldyrev, H. E. Stanley, S. Havlin, Nature Physics, 8, 40
(2012).
[5] W. Li, A. Bashan, S. V. Buldyrev, H. E. Stanley, and S. Havlin
Phys. Rev. Lett. 108, 228702 (2012)
[6] A. Bashan et al, Nature Physics, 9, 667 (2013) |