2,459 research outputs found
Detecting communities of triangles in complex networks using spectral optimization
The study of the sub-structure of complex networks is of major importance to
relate topology and functionality. Many efforts have been devoted to the
analysis of the modular structure of networks using the quality function known
as modularity. However, generally speaking, the relation between topological
modules and functional groups is still unknown, and depends on the semantic of
the links. Sometimes, we know in advance that many connections are transitive
and, as a consequence, triangles have a specific meaning. Here we propose the
study of the modular structure of networks considering triangles as the
building blocks of modules. The method generalizes the standard modularity and
uses spectral optimization to find its maximum. We compare the partitions
obtained with those resulting from the optimization of the standard modularity
in several real networks. The results show that the information reported by the
analysis of modules of triangles complements the information of the classical
modularity analysis.Comment: Computer Communications (in press
Towards realistic artificial benchmark for community detection algorithms evaluation
Assessing the partitioning performance of community detection algorithms is
one of the most important issues in complex network analysis. Artificially
generated networks are often used as benchmarks for this purpose. However,
previous studies showed their level of realism have a significant effect on the
algorithms performance. In this study, we adopt a thorough experimental
approach to tackle this problem and investigate this effect. To assess the
level of realism, we use consensual network topological properties. Based on
the LFR method, the most realistic generative method to date, we propose two
alternative random models to replace the Configuration Model originally used in
this algorithm, in order to increase its realism. Experimental results show
both modifications allow generating collections of community-structured
artificial networks whose topological properties are closer to those
encountered in real-world networks. Moreover, the results obtained with eleven
popular community identification algorithms on these benchmarks show their
performance decrease on more realistic networks
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
Modularity and community structure in networks
Many networks of interest in the sciences, including a variety of social and
biological networks, are found to divide naturally into communities or modules.
The problem of detecting and characterizing this community structure has
attracted considerable recent attention. One of the most sensitive detection
methods is optimization of the quality function known as "modularity" over the
possible divisions of a network, but direct application of this method using,
for instance, simulated annealing is computationally costly. Here we show that
the modularity can be reformulated in terms of the eigenvectors of a new
characteristic matrix for the network, which we call the modularity matrix, and
that this reformulation leads to a spectral algorithm for community detection
that returns results of better quality than competing methods in noticeably
shorter running times. We demonstrate the algorithm with applications to
several network data sets.Comment: 7 pages, 3 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
Detecting highly overlapping community structure by greedy clique expansion
In complex networks it is common for each node to belong to several
communities, implying a highly overlapping community structure. Recent advances
in benchmarking indicate that existing community assignment algorithms that are
capable of detecting overlapping communities perform well only when the extent
of community overlap is kept to modest levels. To overcome this limitation, we
introduce a new community assignment algorithm called Greedy Clique Expansion
(GCE). The algorithm identifies distinct cliques as seeds and expands these
seeds by greedily optimizing a local fitness function. We perform extensive
benchmarks on synthetic data to demonstrate that GCE's good performance is
robust across diverse graph topologies. Significantly, GCE is the only
algorithm to perform well on these synthetic graphs, in which every node
belongs to multiple communities. Furthermore, when put to the task of
identifying functional modules in protein interaction data, and college dorm
assignments in Facebook friendship data, we find that GCE performs
competitively.Comment: 10 pages, 7 Figures. Implementation source and binaries available at
http://sites.google.com/site/greedycliqueexpansion
Modularity functions maximization with nonnegative relaxation facilitates community detection in networks
We show here that the problem of maximizing a family of quantitative
functions, encompassing both the modularity (Q-measure) and modularity density
(D-measure), for community detection can be uniformly understood as a
combinatoric optimization involving the trace of a matrix called modularity
Laplacian. Instead of using traditional spectral relaxation, we apply
additional nonnegative constraint into this graph clustering problem and design
efficient algorithms to optimize the new objective. With the explicit
nonnegative constraint, our solutions are very close to the ideal community
indicator matrix and can directly assign nodes into communities. The
near-orthogonal columns of the solution can be reformulated as the posterior
probability of corresponding node belonging to each community. Therefore, the
proposed method can be exploited to identify the fuzzy or overlapping
communities and thus facilitates the understanding of the intrinsic structure
of networks. Experimental results show that our new algorithm consistently,
sometimes significantly, outperforms the traditional spectral relaxation
approaches
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
Using Triangles to Improve Community Detection in Directed Networks
In a graph, a community may be loosely defined as a group of nodes that are
more closely connected to one another than to the rest of the graph. While
there are a variety of metrics that can be used to specify the quality of a
given community, one common theme is that flows tend to stay within
communities. Hence, we expect cycles to play an important role in community
detection. For undirected graphs, the importance of triangles -- an undirected
3-cycle -- has been known for a long time and can be used to improve community
detection. In directed graphs, the situation is more nuanced. The smallest
cycle is simply two nodes with a reciprocal connection, and using information
about reciprocation has proven to improve community detection. Our new idea is
based on the four types of directed triangles that contain cycles. To identify
communities in directed networks, then, we propose an undirected edge-weighting
scheme based on the type of the directed triangles in which edges are involved.
We also propose a new metric on quality of the communities that is based on the
number of 3-cycles that are split across communities. To demonstrate the impact
of our new weighting, we use the standard METIS graph partitioning tool to
determine communities and show experimentally that the resulting communities
result in fewer 3-cycles being cut. The magnitude of the effect varies between
a 10 and 50% reduction, and we also find evidence that this weighting scheme
improves a task where plausible ground-truth communities are known.Comment: 10 pages, 3 figure
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