17 research outputs found
Networks with time structure from time series
We propose a method of constructing a network, in which its time structure is
directly incorporated, based on a deterministic model from a time series. To
construct such a network, we transform a linear model containing terms with
different time delays into network topology. The terms in the model are
translated into temporal nodes of the network. On each link connecting these
nodes, we assign a positive real number representing the strength of
relationship, or the "distance," between nodes specified by the parameters of
the model. The method is demonstrated by a known system and applied to two
actual time series.Comment: 15 pages, 5 figures, accepted to be published in Physica
Robustness of onion-like correlated networks against targeted attacks
Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108,
3838 (2011)], using simulations, that scale-free networks with "onion
structure" are very robust against targeted high degree attacks. The onion
structure is a network where nodes with almost the same degree are connected.
Motivated by this work, we propose and analyze, based on analytical
considerations, an onion-like candidate for a nearly optimal structure against
simultaneous random and targeted high degree node attacks. The nearly optimal
structure can be viewed as a hierarchically interconnected random regular
graphs, the degrees and populations of which are specified by the degree
distribution. This network structure exhibits an extremely assortative
degree-degree correlation and has a close relationship to the "onion
structure." After deriving a set of exact expressions that enable us to
calculate the critical percolation threshold and the giant component of a
correlated network for an arbitrary type of node removal, we apply the theory
to the cases of random scale-free networks that are highly vulnerable against
targeted high degree node removal. Our results show that this vulnerability can
be significantly reduced by implementing this onion-like type of degree-degree
correlation without much undermining the almost complete robustness against
random node removal. We also investigate in detail the robustness enhancement
due to assortative degree-degree correlation by introducing a joint
degree-degree probability matrix that interpolates between an uncorrelated
network structure and the onion-like structure proposed here by tuning a single
control parameter. The optimal values of the control parameter that maximize
the robustness against simultaneous random and targeted attacks are also
determined. Our analytical calculations are supported by numerical simulations.Comment: 12 pages, 8 figure