292 research outputs found
Communities in Networks
We survey some of the concepts, methods, and applications of community
detection, which has become an increasingly important area of network science.
To help ease newcomers into the field, we provide a guide to available
methodology and open problems, and discuss why scientists from diverse
backgrounds are interested in these problems. As a running theme, we emphasize
the connections of community detection to problems in statistical physics and
computational optimization.Comment: survey/review article on community structure in networks; published
version is available at
http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd
Kantian fractionalization predicts the conflict propensity of the international system
The study of complex social and political phenomena with the perspective and
methods of network science has proven fruitful in a variety of areas, including
applications in political science and more narrowly the field of international
relations. We propose a new line of research in the study of international
conflict by showing that the multiplex fractionalization of the international
system (which we label Kantian fractionalization) is a powerful predictor of
the propensity for violent interstate conflict, a key indicator of the system's
stability. In so doing, we also demonstrate the first use of multislice
modularity for community detection in a multiplex network application. Even
after controlling for established system-level conflict indicators, we find
that Kantian fractionalization contributes more to model fit for violent
interstate conflict than previously established measures. Moreover, evaluating
the influence of each of the constituent networks shows that joint democracy
plays little, if any, role in predicting system stability, thus challenging a
major empirical finding of the international relations literature. Lastly, a
series of Granger causal tests shows that the temporal variability of Kantian
fractionalization is consistent with a causal relationship with the prevalence
of conflict in the international system. This causal relationship has
real-world policy implications as changes in Kantian fractionalization could
serve as an early warning sign of international instability.Comment: 17 pages + 17 pages designed as supplementary online materia
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 Bowl Championship Series: A Mathematical Review
We discuss individual components of the college football Bowl Championship
Series, compare with a simple algorithm defined by random walks on a biased
graph, attempt to predict whether the proposed changes will truly lead to
increased BCS bowl access for non-BCS schools, and conclude by arguing that the
true problem with the BCS Standings lies not in the computer algorithms, but
rather in misguided addition.Comment: 12 pages, 2 figures, submitted to Notices of the AM
Compressing networks with super nodes
Community detection is a commonly used technique for identifying groups in a
network based on similarities in connectivity patterns. To facilitate community
detection in large networks, we recast the network to be partitioned into a
smaller network of 'super nodes', each super node comprising one or more nodes
in the original network. To define the seeds of our super nodes, we apply the
'CoreHD' ranking from dismantling and decycling. We test our approach through
the analysis of two common methods for community detection: modularity
maximization with the Louvain algorithm and maximum likelihood optimization for
fitting a stochastic block model. Our results highlight that applying community
detection to the compressed network of super nodes is significantly faster
while successfully producing partitions that are more aligned with the local
network connectivity, more stable across multiple (stochastic) runs within and
between community detection algorithms, and overlap well with the results
obtained using the full network
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