57 research outputs found
Failure dynamics of the global risk network
Risks threatening modern societies form an intricately interconnected network
that often underlies crisis situations. Yet, little is known about how risk
materializations in distinct domains influence each other. Here we present an
approach in which expert assessments of risks likelihoods and influence
underlie a quantitative model of the global risk network dynamics. The modeled
risks range from environmental to economic and technological and include
difficult to quantify risks, such as geo-political or social. Using the maximum
likelihood estimation, we find the optimal model parameters and demonstrate
that the model including network effects significantly outperforms the others,
uncovering full value of the expert collected data. We analyze the model
dynamics and study its resilience and stability. Our findings include such risk
properties as contagion potential, persistence, roles in cascades of failures
and the identity of risks most detrimental to system stability. The model
provides quantitative means for measuring the adverse effects of risk
interdependence and the materialization of risks in the network
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
Resilience of Complex Networks to Random Breakdown
Using Monte Carlo simulations we calculate , the fraction of nodes which
are randomly removed before global connectivity is lost, for networks with
scale-free and bimodal degree distributions. Our results differ with the
results predicted by an equation for proposed by Cohen, et al. We discuss
the reasons for this disagreement and clarify the domain for which the proposed
equation is valid
Communication Bottlenecks in Scale-Free Networks
We consider the effects of network topology on the optimality of packet
routing quantified by , the rate of packet insertion beyond which
congestion and queue growth occurs. The key result of this paper is to show
that for any network, there exists an absolute upper bound, expressed in terms
of vertex separators, for the scaling of with network size ,
irrespective of the routing algorithm used. We then derive an estimate to this
upper bound for scale-free networks, and introduce a novel static routing
protocol which is superior to shortest path routing under intense packet
insertion rates.Comment: 5 pages, 3 figure
The Approximate Invariance of the Average Number of Connections for the Continuum Percolation of Squares at Criticality
We perform Monte Carlo simulations to determine the average excluded area
and Monte Carlo simulation results for the percolation threshold, we
estimate the mean number of connections per object at the percolation
threshold for squares in 2-D. We study systems of squares that are allowed
random orientations within a specified angular interval. Our simulations show
that the variation in is within 1.6% when the angular interval is varied
from 0 to
Graph Partitioning Induced Phase Transitions
We study the percolation properties of graph partitioning on random regular
graphs with N vertices of degree . Optimal graph partitioning is directly
related to optimal attack and immunization of complex networks. We find that
for any partitioning process (even if non-optimal) that partitions the graph
into equal sized connected components (clusters), the system undergoes a
percolation phase transition at where is the fraction of
edges removed to partition the graph. For optimal partitioning, at the
percolation threshold, we find where is the size of the
clusters and where is their diameter. Additionally,
we find that undergoes multiple non-percolation transitions for
Scale-Free Networks Emerging from Weighted Random Graphs
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with
each link. We generate a new ``Supernode network'' by merging all nodes
connected by links having weights below the percolation threshold (percolation
clusters) into a single node. We show that this network is scale-free, i.e.,
the degree distribution is with . Our
results imply that the minimum spanning tree (MST) in random graphs is composed
of percolation clusters, which are interconnected by a set of links that create
a scale-free tree with . We show that optimization causes the
percolation threshold to emerge spontaneously, thus creating naturally a
scale-free ``supernode network''. We discuss the possibility that this
phenomenon is related to the evolution of several real world scale-free
networks
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