22,909 research outputs found
Robustness and modular structure in networks
Complex networks have recently attracted much interest due to their
prevalence in nature and our daily lives [1, 2]. A critical property of a
network is its resilience to random breakdown and failure [3-6], typically
studied as a percolation problem [7-9] or by modeling cascading failures
[10-12]. Many complex systems, from power grids and the Internet to the brain
and society [13-15], can be modeled using modular networks comprised of small,
densely connected groups of nodes [16, 17]. These modules often overlap, with
network elements belonging to multiple modules [18, 19]. Yet existing work on
robustness has not considered the role of overlapping, modular structure. Here
we study the robustness of these systems to the failure of elements. We show
analytically and empirically that it is possible for the modules themselves to
become uncoupled or non-overlapping well before the network disintegrates. If
overlapping modular organization plays a role in overall functionality,
networks may be far more vulnerable than predicted by conventional percolation
theory.Comment: 14 pages, 9 figure
Extracting the hierarchical organization of complex systems
Extracting understanding from the growing ``sea'' of biological and
socio-economic data is one of the most pressing scientific challenges facing
us. Here, we introduce and validate an unsupervised method that is able to
accurately extract the hierarchical organization of complex biological, social,
and technological networks. We define an ensemble of hierarchically nested
random graphs, which we use to validate the method. We then apply our method to
real-world networks, including the air-transportation network, an electronic
circuit, an email exchange network, and metabolic networks. We find that our
method enables us to obtain an accurate multi-scale descriptions of a complex
system.Comment: Figures in screen resolution. Version with full resolution figures
available at
http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd
AUGUR: Forecasting the Emergence of New Research Topics
Being able to rapidly recognise new research trends is strategic for many stakeholders, including universities, institutional funding bodies, academic publishers and companies. The literature presents several approaches to identifying the emergence of new research topics, which rely on the assumption that the topic is already exhibiting a certain degree of popularity and consistently referred to by a community of researchers. However, detecting the emergence of a new research area at an embryonic stage, i.e., before the topic has been consistently labelled by a community of researchers and associated with a number of publications, is still an open challenge. We address this issue by introducing Augur, a novel approach to the early detection of research topics. Augur analyses the diachronic relationships between research areas and is able to detect clusters of topics that exhibit dynamics correlated with the emergence of new research topics. Here we also present the Advanced Clique Percolation Method (ACPM), a new community detection algorithm developed specifically for supporting this task. Augur was evaluated on a gold standard of 1,408 debutant topics in the 2000-2011 interval and outperformed four alternative approaches in terms of both precision and recall
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
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
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