9,769 research outputs found
Robustness surfaces of complex networks
Despite the robustness of complex networks has been extensively studied in
the last decade, there still lacks a unifying framework able to embrace all the
proposed metrics. In the literature there are two open issues related to this
gap: (a) how to dimension several metrics to allow their summation and (b) how
to weight each of the metrics. In this work we propose a solution for the two
aforementioned problems by defining the -value and introducing the concept
of \emph{robustness surface} (). The rationale of our proposal is to
make use of Principal Component Analysis (PCA). We firstly adjust to 1 the
initial robustness of a network. Secondly, we find the most informative
robustness metric under a specific failure scenario. Then, we repeat the
process for several percentage of failures and different realizations of the
failure process. Lastly, we join these values to form the robustness surface,
which allows the visual assessment of network robustness variability. Results
show that a network presents different robustness surfaces (i.e., dissimilar
shapes) depending on the failure scenario and the set of metrics. In addition,
the robustness surface allows the robustness of different networks to be
compared.Comment: submitted to Scientific Report
Dynamic Effects Increasing Network Vulnerability to Cascading Failures
We study cascading failures in networks using a dynamical flow model based on
simple conservation and distribution laws to investigate the impact of
transient dynamics caused by the rebalancing of loads after an initial network
failure (triggering event). It is found that considering the flow dynamics may
imply reduced network robustness compared to previous static overload failure
models. This is due to the transient oscillations or overshooting in the loads,
when the flow dynamics adjusts to the new (remaining) network structure. We
obtain {\em upper} and {\em lower} limits to network robustness, and it is
shown that {\it two} time scales and , defined by the network
dynamics, are important to consider prior to accurately addressing network
robustness or vulnerability. The robustness of networks showing cascading
failures is generally determined by a complex interplay between the network
topology and flow dynamics, where the ratio determines the
relative role of the two of them.Comment: 4 pages Latex, 4 figure
Accelerating Consensus by Spectral Clustering and Polynomial Filters
It is known that polynomial filtering can accelerate the convergence towards
average consensus on an undirected network. In this paper the gain of a
second-order filtering is investigated. A set of graphs is determined for which
consensus can be attained in finite time, and a preconditioner is proposed to
adapt the undirected weights of any given graph to achieve fastest convergence
with the polynomial filter. The corresponding cost function differs from the
traditional spectral gap, as it favors grouping the eigenvalues in two
clusters. A possible loss of robustness of the polynomial filter is also
highlighted
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