65,840 research outputs found
Robustness and modular structure in networks
Complex networks have recently attracted much interest due to their
prevalence in nature and our daily lives [1, 2]. A critical property of a
network is its resilience to random breakdown and failure [3-6], typically
studied as a percolation problem [7-9] or by modeling cascading failures
[10-12]. Many complex systems, from power grids and the Internet to the brain
and society [13-15], can be modeled using modular networks comprised of small,
densely connected groups of nodes [16, 17]. These modules often overlap, with
network elements belonging to multiple modules [18, 19]. Yet existing work on
robustness has not considered the role of overlapping, modular structure. Here
we study the robustness of these systems to the failure of elements. We show
analytically and empirically that it is possible for the modules themselves to
become uncoupled or non-overlapping well before the network disintegrates. If
overlapping modular organization plays a role in overall functionality,
networks may be far more vulnerable than predicted by conventional percolation
theory.Comment: 14 pages, 9 figure
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
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