remarks_on_lectures

Lectures on Complex Networks - remarks

Remarks

to the book companion site

Corrections:

• • p. 48, bookmark 11 ... ... ... >>>----->>> $\lambda_c=0$ for the SIS model on random networks.

  • p. 85, line 8: observe a slower decay >>>----->>> observe a faster decay

  • p. 94, line 3: subsequent intervals >>>----->>> subsequent ones

  • p. 99, Sec. 13.1, line 1: (1900-1988) >>>----->>> (1900-1998) [E. Ising]

Details:

• • p. 48 The SIS model. It turns out that the SIS model has a finite epidemic threshold only on lattices (regular and disordered). In the networks with slowly and rapidly decaying degree distributions, even in the classical random graphs, there is no epidemic threshold for this model (!) [Y. Wang, D. Chakrabarti, C. Wang, and C. Faloutsos, 22nd International Symposium on Reliable Distributed Systems (SRDS’03) (2003), pp. 25–34; C. Castellano and R. Pastor-Satorras, arXiv:1010.1646 ]. (ZERO!) So in bookmark 11 on p. 48, it should be "$\lambda_c=0$ for the SIS model on random networks" instead of the expression in the book, which was obtained only for annealed networks.

  • p. 68 Funneling effect.

  • p. 116 Explosive percolation. After the book was published we found that, in contrast to the first conclusions based on computer experiments, "Explosive percolation" transition is actually continuous, (!!!) R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, arXiv:1009.2534. This is a second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We obtained these, I believe, very interesting and strong results by analyzing infinite systems. As far as I know, no transitions of this kind (a unique set of critical exponents, dimensions and properties) were observed previously. Thus there is no explosion at the "explosive percolation" transition! See the paper.