Evolution of Networks
to home page
New results:
• An extensive review about of critical phenomena in complex networks and in interacting systems on them
Note that the condmat version of the review is essentially more detailed and comprehensive than the Rev. Mod. Phys. version.
Critical phenomena in complex networks,
A.V. Goltsev, S.N. Dorogovtsev, and J.F.F. Mendes,
Rev. Mod. Phys. , (2008);
arXiv:0705.0010 [condmat].
• Transition from infinite to finitedimensional system
We have analytically resolved this nontrivial problem for a generalization of random recursive trees where a probability of attachment to an existing vertex depends on its age.
Transition from small to large world in growing networks,
S. N. Dorogovtsev, P. L. Krapivsky, and J. F. F. Mendes,
EPL 81, 30004 15 (2008);
arXiv:0709.3094 [condmat].
• Laplacian spectra of complex networks and random walks on them
We resolved this problem for sparse uncorrelated networks. The results  the Laplacian spectrum near the lower boundary and the asymptotics of the autocorrelator  are determined by the minimum degrees in a network. Unfortunately, these asymptotics can be observed only in astronomically large networks.
Laplacian spectra of complex networks and random walks on them: Are scalefree architectures really important?,
A. N. Samukhin, S. N. Dorogovtsev, and J. F. F. Mendes,
Phys. Rev. E , (2008);
arXiv:0706.1176 [condmat].
Sergey Dorogovtsev
