20,666 research outputs found
Localization and Spreading of Diseases in Complex Networks
Using the SIS model on unweighted and weighted networks, we consider the disease localizationphenomenon. In contrast to the well-recognized point of view that diseases infect a finite fractionof vertices right above the epidemic threshold, we show that diseases can be localized on a finitenumber of vertices, where hubs and edges with large weights are centers of localization. Our resultsfollow from the analysis of standard models of networks and empirical data for real-world networks
Disease Localization in Multilayer Networks
We present a continuous formulation of epidemic spreading on multilayer
networks using a tensorial representation, extending the models of monoplex
networks to this context. We derive analytical expressions for the epidemic
threshold of the SIS and SIR dynamics, as well as upper and lower bounds for
the disease prevalence in the steady state for the SIS scenario. Using the
quasi-stationary state method we numerically show the existence of disease
localization and the emergence of two or more susceptibility peaks, which are
characterized analytically and numerically through the inverse participation
ratio. Furthermore, when mapping the critical dynamics to an eigenvalue
problem, we observe a characteristic transition in the eigenvalue spectra of
the supra-contact tensor as a function of the ratio of two spreading rates: if
the rate at which the disease spreads within a layer is comparable to the
spreading rate across layers, the individual spectra of each layer merge with
the coupling between layers. Finally, we verified the barrier effect, i.e., for
three-layer configuration, when the layer with the largest eigenvalue is
located at the center of the line, it can effectively act as a barrier to the
disease. The formalism introduced here provides a unifying mathematical
approach to disease contagion in multiplex systems opening new possibilities
for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure
Griffiths phases and localization in hierarchical modular networks
We study variants of hierarchical modular network models suggested by Kaiser
and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional
brain connectivity, using extensive simulations and quenched mean-field theory
(QMF), focusing on structures with a connection probability that decays
exponentially with the level index. Such networks can be embedded in
two-dimensional Euclidean space. We explore the dynamic behavior of the contact
process (CP) and threshold models on networks of this kind, including
hierarchical trees. While in the small-world networks originally proposed to
model brain connectivity, the topological heterogeneities are not strong enough
to induce deviations from mean-field behavior, we show that a Griffiths phase
can emerge under reduced connection probabilities, approaching the percolation
threshold. In this case the topological dimension of the networks is finite,
and extended regions of bursty, power-law dynamics are observed. Localization
in the steady state is also shown via QMF. We investigate the effects of link
asymmetry and coupling disorder, and show that localization can occur even in
small-world networks with high connectivity in case of link disorder.Comment: 18 pages, 20 figures, accepted version in Scientific Report
Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
The largest eigenvalue of a network's adjacency matrix and its associated
principal eigenvector are key elements for determining the topological
structure and the properties of dynamical processes mediated by it. We present
a physically grounded expression relating the value of the largest eigenvalue
of a given network to the largest eigenvalue of two network subgraphs,
considered as isolated: The hub with its immediate neighbors and the densely
connected set of nodes with maximum -core index. We validate this formula
showing that it predicts with good accuracy the largest eigenvalue of a large
set of synthetic and real-world topologies. We also present evidence of the
consequences of these findings for broad classes of dynamics taking place on
the networks. As a byproduct, we reveal that the spectral properties of
heterogeneous networks built according to the linear preferential attachment
model are qualitatively different from those of their static counterparts.Comment: 18 pages, 13 figure
A survey on Human Mobility and its applications
Human Mobility has attracted attentions from different fields of studies such
as epidemic modeling, traffic engineering, traffic prediction and urban
planning. In this survey we review major characteristics of human mobility
studies including from trajectory-based studies to studies using graph and
network theory. In trajectory-based studies statistical measures such as jump
length distribution and radius of gyration are analyzed in order to investigate
how people move in their daily life, and if it is possible to model this
individual movements and make prediction based on them. Using graph in mobility
studies, helps to investigate the dynamic behavior of the system, such as
diffusion and flow in the network and makes it easier to estimate how much one
part of the network influences another by using metrics like centrality
measures. We aim to study population flow in transportation networks using
mobility data to derive models and patterns, and to develop new applications in
predicting phenomena such as congestion. Human Mobility studies with the new
generation of mobility data provided by cellular phone networks, arise new
challenges such as data storing, data representation, data analysis and
computation complexity. A comparative review of different data types used in
current tools and applications of Human Mobility studies leads us to new
approaches for dealing with mentioned challenges
Network centrality: an introduction
Centrality is a key property of complex networks that influences the behavior
of dynamical processes, like synchronization and epidemic spreading, and can
bring important information about the organization of complex systems, like our
brain and society. There are many metrics to quantify the node centrality in
networks. Here, we review the main centrality measures and discuss their main
features and limitations. The influence of network centrality on epidemic
spreading and synchronization is also pointed out in this chapter. Moreover, we
present the application of centrality measures to understand the function of
complex systems, including biological and cortical networks. Finally, we
discuss some perspectives and challenges to generalize centrality measures for
multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A
Mathematical modeling approach" by Springe
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