836 research outputs found
Immunization for complex network based on the effective degree of vertex
The basic idea of many effective immunization strategies is first to rank the
importance of vertices according to the degrees of vertices and then remove the
vertices from highest importance to lowest until the network becomes
disconnected. Here we define the effective degrees of vertex, i.e., the number
of its connections linking to un-immunized nodes in current network during the
immunization procedure, to rank the importance of vertex, and modify these
strategies by using the effective degrees of vertices. Simulations on both the
scale-free network models with various degree correlations and two real
networks have revealed that the immunization strategies based on the effective
degrees are often more effective than those based on the degrees in the initial
network.Comment: 16 pages, 5 figure
Recoverable prevalence in growing scale-free networks and the effective immunization
We study the persistent recoverable prevalence and the extinction of computer
viruses via e-mails on a growing scale-free network with new users, which
structure is estimated form real data. The typical phenomenon is simulated in a
realistic model with the probabilistic execution and detection of viruses.
Moreover, the conditions of extinction by random and targeted immunizations for
hubs are derived through bifurcation analysis for simpler models by using a
mean-field approximation without the connectivity correlations. We can
qualitatively understand the mechanisms of the spread in linearly growing
scale-free networks.Comment: 9 pages, 9 figures, 1 table. Update version after helpful referee
comment
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Immunization of Real Complex Communication Networks
Most communication networks are complex. In this paper, we address one of the
fundamental problems we are facing nowadays, namely, how we can efficiently
protect these networks. To this end, we study an immunization strategy and
found that it works as good as targeted immunization, but using only local
information about the network topology. Our findings are supported with
numerical simulations of the Susceptible-Infected-Removed (SIR) model on top of
real communication networks, where immune nodes are previously identified by a
covering algorithm. The results provide useful hints in the way to design and
deploying a digital immune system.Comment: 6 pages. To appear in the European Physical Journal B (2006
Reactive immunization on complex networks
Epidemic spreading on complex networks depends on the topological structure
as well as on the dynamical properties of the infection itself. Generally
speaking, highly connected individuals play the role of hubs and are crucial to
channel information across the network. On the other hand, static topological
quantities measuring the connectivity structure are independent on the
dynamical mechanisms of the infection. A natural question is therefore how to
improve the topological analysis by some kind of dynamical information that may
be extracted from the ongoing infection itself. In this spirit, we propose a
novel vaccination scheme that exploits information from the details of the
infection pattern at the moment when the vaccination strategy is applied.
Numerical simulations of the infection process show that the proposed
immunization strategy is effective and robust on a wide class of complex
networks
Dynamical patterns of epidemic outbreaks in complex heterogeneous networks
We present a thorough inspection of the dynamical behavior of epidemic
phenomena in populations with complex and heterogeneous connectivity patterns.
We show that the growth of the epidemic prevalence is virtually instantaneous
in all networks characterized by diverging degree fluctuations, independently
of the structure of the connectivity correlation functions characterizing the
population network. By means of analytical and numerical results, we show that
the outbreak time evolution follows a precise hierarchical dynamics. Once
reached the most highly connected hubs, the infection pervades the network in a
progressive cascade across smaller degree classes. Finally, we show the
influence of the initial conditions and the relevance of statistical results in
single case studies concerning heterogeneous networks. The emerging theoretical
framework appears of general interest in view of the recently observed
abundance of natural networks with complex topological features and might
provide useful insights for the development of adaptive strategies aimed at
epidemic containment.Comment: 13 pages, 11 figure
Generalized Network Dismantling
Finding the set of nodes, which removed or (de)activated can stop the spread
of (dis)information, contain an epidemic or disrupt the functioning of a
corrupt/criminal organization is still one of the key challenges in network
science. In this paper, we introduce the generalized network dismantling
problem, which aims to find the set of nodes that, when removed from a network,
results in a network fragmentation into subcritical network components at
minimum cost. For unit costs, our formulation becomes equivalent to the
standard network dismantling problem. Our non-unit cost generalization allows
for the inclusion of topological cost functions related to node centrality and
non-topological features such as the price, protection level or even social
value of a node. In order to solve this optimization problem, we propose a
method, which is based on the spectral properties of a novel node-weighted
Laplacian operator. The proposed method is applicable to large-scale networks
with millions of nodes. It outperforms current state-of-the-art methods and
opens new directions in understanding the vulnerability and robustness of
complex systems.Comment: 6 pages, 5 figure
Velocity and hierarchical spread of epidemic outbreaks in scale-free networks
We study the effect of the connectivity pattern of complex networks on the
propagation dynamics of epidemics. The growth time scale of outbreaks is
inversely proportional to the network degree fluctuations, signaling that
epidemics spread almost instantaneously in networks with scale-free degree
distributions. This feature is associated with an epidemic propagation that
follows a precise hierarchical dynamics. Once the highly connected hubs are
reached, the infection pervades the network in a progressive cascade across
smaller degree classes. The present results are relevant for the development of
adaptive containment strategies.Comment: 4 pages, 4 figures, final versio
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