1,179 research outputs found
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
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
Theories for influencer identification in complex networks
In social and biological systems, the structural heterogeneity of interaction
networks gives rise to the emergence of a small set of influential nodes, or
influencers, in a series of dynamical processes. Although much smaller than the
entire network, these influencers were observed to be able to shape the
collective dynamics of large populations in different contexts. As such, the
successful identification of influencers should have profound implications in
various real-world spreading dynamics such as viral marketing, epidemic
outbreaks and cascading failure. In this chapter, we first summarize the
centrality-based approach in finding single influencers in complex networks,
and then discuss the more complicated problem of locating multiple influencers
from a collective point of view. Progress rooted in collective influence
theory, belief-propagation and computer science will be presented. Finally, we
present some applications of influencer identification in diverse real-world
systems, including online social platforms, scientific publication, brain
networks and socioeconomic systems.Comment: 24 pages, 6 figure
Network-based brain computer interfaces: principles and applications
Brain-computer interfaces (BCIs) make possible to interact with the external
environment by decoding the mental intention of individuals. BCIs can therefore
be used to address basic neuroscience questions but also to unlock a variety of
applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In
general, BCI usability critically depends on the ability to comprehensively
characterize brain functioning and correctly identify the user s mental state.
To this end, much of the efforts have focused on improving the classification
algorithms taking into account localized brain activities as input features.
Despite considerable improvement BCI performance is still unstable and, as a
matter of fact, current features represent oversimplified descriptors of brain
functioning. In the last decade, growing evidence has shown that the brain
works as a networked system composed of multiple specialized and spatially
distributed areas that dynamically integrate information. While more complex,
looking at how remote brain regions functionally interact represents a grounded
alternative to better describe brain functioning. Thanks to recent advances in
network science, i.e. a modern field that draws on graph theory, statistical
mechanics, data mining and inferential modelling, scientists have now powerful
means to characterize complex brain networks derived from neuroimaging data.
Notably, summary features can be extracted from these networks to
quantitatively measure specific organizational properties across a variety of
topological scales. In this topical review, we aim to provide the
state-of-the-art supporting the development of a network theoretic approach as
a promising tool for understanding BCIs and improve usability
Super-resolution community detection for layer-aggregated multilayer networks
Applied network science often involves preprocessing network data before
applying a network-analysis method, and there is typically a theoretical
disconnect between these steps. For example, it is common to aggregate
time-varying network data into windows prior to analysis, and the tradeoffs of
this preprocessing are not well understood. Focusing on the problem of
detecting small communities in multilayer networks, we study the effects of
layer aggregation by developing random-matrix theory for modularity matrices
associated with layer-aggregated networks with nodes and layers, which
are drawn from an ensemble of Erd\H{o}s-R\'enyi networks. We study phase
transitions in which eigenvectors localize onto communities (allowing their
detection) and which occur for a given community provided its size surpasses a
detectability limit . When layers are aggregated via a summation, we
obtain , where is the number of
layers across which the community persists. Interestingly, if is allowed to
vary with then summation-based layer aggregation enhances small-community
detection even if the community persists across a vanishing fraction of layers,
provided that decays more slowly than . Moreover,
we find that thresholding the summation can in some cases cause to decay
exponentially, decreasing by orders of magnitude in a phenomenon we call
super-resolution community detection. That is, layer aggregation with
thresholding is a nonlinear data filter enabling detection of communities that
are otherwise too small to detect. Importantly, different thresholds generally
enhance the detectability of communities having different properties,
illustrating that community detection can be obscured if one analyzes network
data using a single threshold.Comment: 11 pages, 8 figure
The spatial component of R&D networks
We study the role of geography in R&D networks by means of a quantitative,
micro-geographic approach. Using a large database that covers international R&D
collaborations from 1984 to 2009, we localize each actor precisely in space
through its latitude and longitude. This allows us to analyze the R&D network
at all geographic scales simultaneously. Our empirical results show that
despite the high importance of the city level, transnational R&D collaborations
at large distances are much more frequent than expected from similar networks.
This provides evidence for the ambiguity of distance in economic cooperation
which is also suggested by the existing literature. In addition we test whether
the hypothesis of local buzz and global pipelines applies to the observed R&D
network by calculating well-defined metrics from network theory.Comment: Working paper, 22 pages, 7 figure
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