3,226 research outputs found
Infrastructure network vulnerability
The work presented in this paper aims to propose a methodology of analyzing infrastructure network vulnerability in the field of prevention or reduction of the natural disaster consequences. After a state of the art on vulnerability models in the academic literature, the various vulnerability factors are classified and discussed. Eventually, a general model of vulnerability analysis including societal parameters is presented
Cascading failures in spatially-embedded random networks
Cascading failures constitute an important vulnerability of interconnected
systems. Here we focus on the study of such failures on networks in which the
connectivity of nodes is constrained by geographical distance. Specifically, we
use random geometric graphs as representative examples of such spatial
networks, and study the properties of cascading failures on them in the
presence of distributed flow. The key finding of this study is that the process
of cascading failures is non-self-averaging on spatial networks, and thus,
aggregate inferences made from analyzing an ensemble of such networks lead to
incorrect conclusions when applied to a single network, no matter how large the
network is. We demonstrate that this lack of self-averaging disappears with the
introduction of a small fraction of long-range links into the network. We
simulate the well studied preemptive node removal strategy for cascade
mitigation and show that it is largely ineffective in the case of spatial
networks. We introduce an altruistic strategy designed to limit the loss of
network nodes in the event of a cascade triggering failure and show that it
performs better than the preemptive strategy. Finally, we consider a real-world
spatial network viz. a European power transmission network and validate that
our findings from the study of random geometric graphs are also borne out by
simulations of cascading failures on the empirical network.Comment: 13 pages, 15 figure
Inhomogeneous percolation models for spreading phenomena in random graphs
Percolation theory has been largely used in the study of structural
properties of complex networks such as the robustness, with remarkable results.
Nevertheless, a purely topological description is not sufficient for a correct
characterization of networks behaviour in relation with physical flows and
spreading phenomena taking place on them. The functionality of real networks
also depends on the ability of the nodes and the edges in bearing and handling
loads of flows, energy, information and other physical quantities. We propose
to study these properties introducing a process of inhomogeneous percolation,
in which both the nodes and the edges spread out the flows with a given
probability.
Generating functions approach is exploited in order to get a generalization
of the Molloy-Reed Criterion for inhomogeneous joint site bond percolation in
correlated random graphs. A series of simple assumptions allows the analysis of
more realistic situations, for which a number of new results are presented. In
particular, for the site percolation with inhomogeneous edge transmission, we
obtain the explicit expressions of the percolation threshold for many
interesting cases, that are analyzed by means of simple examples and numerical
simulations. Some possible applications are debated.Comment: 28 pages, 11 figure
Efficiency of Scale-Free Networks: Error and Attack Tolerance
The concept of network efficiency, recently proposed to characterize the
properties of small-world networks, is here used to study the effects of errors
and attacks on scale-free networks. Two different kinds of scale-free networks,
i.e. networks with power law P(k), are considered: 1) scale-free networks with
no local clustering produced by the Barabasi-Albert model and 2) scale-free
networks with high clustering properties as in the model by Klemm and Eguiluz,
and their properties are compared to the properties of random graphs
(exponential graphs). By using as mathematical measures the global and the
local efficiency we investigate the effects of errors and attacks both on the
global and the local properties of the network. We show that the global
efficiency is a better measure than the characteristic path length to describe
the response of complex networks to external factors. We find that, at variance
with random graphs, scale-free networks display, both on a global and on a
local scale, a high degree of error tolerance and an extreme vulnerability to
attacks. In fact, the global and the local efficiency are unaffected by the
failure of some randomly chosen nodes, though they are extremely sensititive to
the removal of the few nodes which play a crucial role in maintaining the
network's connectivity.Comment: 23 pages, 10 figure
Robustness of Random Graphs Based on Natural Connectivity
Recently, it has been proposed that the natural connectivity can be used to
efficiently characterise the robustness of complex networks. Natural
connectivity quantifies the redundancy of alternative routes in a network by
evaluating the weighted number of closed walks of all lengths and can be
regarded as the average eigenvalue obtained from the graph spectrum. In this
article, we explore the natural connectivity of random graphs both analytically
and numerically and show that it increases linearly with the average degree. By
comparing with regular ring lattices and random regular graphs, we show that
random graphs are more robust than random regular graphs; however, the
relationship between random graphs and regular ring lattices depends on the
average degree and graph size. We derive the critical graph size as a function
of the average degree, which can be predicted by our analytical results. When
the graph size is less than the critical value, random graphs are more robust
than regular ring lattices, whereas regular ring lattices are more robust than
random graphs when the graph size is greater than the critical value.Comment: 12 pages, 4 figure
Effect of edge removal on topological and functional robustness of complex networks
We study the robustness of complex networks subject to edge removal. Several
network models and removing strategies are simulated. Rather than the existence
of the giant component, we use total connectedness as the criterion of
breakdown. The network topologies are introduced a simple traffic dynamics and
the total connectedness is interpreted not only in the sense of topology but
also in the sense of function. We define the topological robustness and the
functional robustness, investigate their combined effect and compare their
relative importance to each other. The results of our study provide an
alternative view of the overall robustness and highlight efficient ways to
improve the robustness of the network models.Comment: 21 pages, 9 figure
The Price of Anarchy for Network Formation in an Adversary Model
We study network formation with n players and link cost \alpha > 0. After the
network is built, an adversary randomly deletes one link according to a certain
probability distribution. Cost for player v incorporates the expected number of
players to which v will become disconnected. We show existence of equilibria
and a price of stability of 1+o(1) under moderate assumptions on the adversary
and n \geq 9.
As the main result, we prove bounds on the price of anarchy for two special
adversaries: one removes a link chosen uniformly at random, while the other
removes a link that causes a maximum number of player pairs to be separated.
For unilateral link formation we show a bound of O(1) on the price of anarchy
for both adversaries, the constant being bounded by 10+o(1) and 8+o(1),
respectively. For bilateral link formation we show O(1+\sqrt{n/\alpha}) for one
adversary (if \alpha > 1/2), and \Theta(n) for the other (if \alpha > 2
considered constant and n \geq 9). The latter is the worst that can happen for
any adversary in this model (if \alpha = \Omega(1)). This points out
substantial differences between unilateral and bilateral link formation
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