53,070 research outputs found
A General Definition of Network Communities and the Corresponding Detection Algorithm
Network structures, consisting of nodes and edges, have applications in
almost all subjects. A set of nodes is called a community if the nodes have
strong interrelations. Industries (including cell phone carriers and online
social media companies) need community structures to allocate network resources
and provide proper and accurate services. However, all the current detection
algorithms are motivated by the practical problems, whose applicabilities in
other fields are open to question. Thence, for a new community problem,
researchers need to derive algorithms ad hoc, which is arduous and even
unnecessary. In this paper, we represent a general procedure to find community
structures in practice. We mainly focus on two typical types of networks:
transmission networks and similarity networks. We reduce them to a unified
graph model, based on which we propose a general method to define and detect
communities. Readers can specialize our general algorithm to accommodate their
problems. In the end, we also give a demonstration to show how the algorithm
works
Defining and identifying communities in networks
The investigation of community structures in networks is an important issue
in many domains and disciplines. This problem is relevant for social tasks
(objective analysis of relationships on the web), biological inquiries
(functional studies in metabolic, cellular or protein networks) or
technological problems (optimization of large infrastructures). Several types
of algorithm exist for revealing the community structure in networks, but a
general and quantitative definition of community is still lacking, leading to
an intrinsic difficulty in the interpretation of the results of the algorithms
without any additional non-topological information. In this paper we face this
problem by introducing two quantitative definitions of community and by showing
how they are implemented in practice in the existing algorithms. In this way
the algorithms for the identification of the community structure become fully
self-contained. Furthermore, we propose a new local algorithm to detect
communities which outperforms the existing algorithms with respect to the
computational cost, keeping the same level of reliability. The new algorithm is
tested on artificial and real-world graphs. In particular we show the
application of the new algorithm to a network of scientific collaborations,
which, for its size, can not be attacked with the usual methods. This new class
of local algorithms could open the way to applications to large-scale
technological and biological applications.Comment: Revtex, final form, 14 pages, 6 figure
Community detection for correlation matrices
A challenging problem in the study of complex systems is that of resolving,
without prior information, the emergent, mesoscopic organization determined by
groups of units whose dynamical activity is more strongly correlated internally
than with the rest of the system. The existing techniques to filter
correlations are not explicitly oriented towards identifying such modules and
can suffer from an unavoidable information loss. A promising alternative is
that of employing community detection techniques developed in network theory.
Unfortunately, this approach has focused predominantly on replacing network
data with correlation matrices, a procedure that tends to be intrinsically
biased due to its inconsistency with the null hypotheses underlying the
existing algorithms. Here we introduce, via a consistent redefinition of null
models based on random matrix theory, the appropriate correlation-based
counterparts of the most popular community detection techniques. Our methods
can filter out both unit-specific noise and system-wide dependencies, and the
resulting communities are internally correlated and mutually anti-correlated.
We also implement multiresolution and multifrequency approaches revealing
hierarchically nested sub-communities with `hard' cores and `soft' peripheries.
We apply our techniques to several financial time series and identify
mesoscopic groups of stocks which are irreducible to a standard, sectorial
taxonomy, detect `soft stocks' that alternate between communities, and discuss
implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR
Community Detection via Maximization of Modularity and Its Variants
In this paper, we first discuss the definition of modularity (Q) used as a
metric for community quality and then we review the modularity maximization
approaches which were used for community detection in the last decade. Then, we
discuss two opposite yet coexisting problems of modularity optimization: in
some cases, it tends to favor small communities over large ones while in
others, large communities over small ones (so called the resolution limit
problem). Next, we overview several community quality metrics proposed to solve
the resolution limit problem and discuss Modularity Density (Qds) which
simultaneously avoids the two problems of modularity. Finally, we introduce two
novel fine-tuned community detection algorithms that iteratively attempt to
improve the community quality measurements by splitting and merging the given
network community structure. The first of them, referred to as Fine-tuned Q, is
based on modularity (Q) while the second one is based on Modularity Density
(Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of
modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds
on four real networks, and also on the classical clique network and the LFR
benchmark networks, each of which is instantiated by a wide range of
parameters. The results indicate that Fine-tuned Qds is the most effective
among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can
be applied to the communities detected by other algorithms to significantly
improve their results
A shadowing problem in the detection of overlapping communities: lifting the resolution limit through a cascading procedure
Community detection is the process of assigning nodes and links in
significant communities (e.g. clusters, function modules) and its development
has led to a better understanding of complex networks. When applied to sizable
networks, we argue that most detection algorithms correctly identify prominent
communities, but fail to do so across multiple scales. As a result, a
significant fraction of the network is left uncharted. We show that this
problem stems from larger or denser communities overshadowing smaller or
sparser ones, and that this effect accounts for most of the undetected
communities and unassigned links. We propose a generic cascading approach to
community detection that circumvents the problem. Using real and artificial
network datasets with three widely used community detection algorithms, we show
how a simple cascading procedure allows for the detection of the missing
communities. This work highlights a new detection limit of community structure,
and we hope that our approach can inspire better community detection
algorithms.Comment: 14 pages, 12 figures + supporting information (5 pages, 6 tables, 3
figures
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