2,045 research outputs found
Hierarchical multiresolution method to overcome the resolution limit in complex networks
The analysis of the modular structure of networks is a major challenge in
complex networks theory. The validity of the modular structure obtained is
essential to confront the problem of the topology-functionality relationship.
Recently, several authors have worked on the limit of resolution that different
community detection algorithms have, making impossible the detection of natural
modules when very different topological scales coexist in the network. Existing
multiresolution methods are not the panacea for solving the problem in extreme
situations, and also fail. Here, we present a new hierarchical multiresolution
scheme that works even when the network decomposition is very close to the
resolution limit. The idea is to split the multiresolution method for optimal
subgraphs of the network, focusing the analysis on each part independently. We
also propose a new algorithm to speed up the computational cost of screening
the mesoscale looking for the resolution parameter that best splits every
subgraph. The hierarchical algorithm is able to solve a difficult benchmark
proposed in [Lancichinetti & Fortunato, 2011], encouraging the further analysis
of hierarchical methods based on the modularity quality function
Router-level community structure of the Internet Autonomous Systems
The Internet is composed of routing devices connected between them and
organized into independent administrative entities: the Autonomous Systems. The
existence of different types of Autonomous Systems (like large connectivity
providers, Internet Service Providers or universities) together with
geographical and economical constraints, turns the Internet into a complex
modular and hierarchical network. This organization is reflected in many
properties of the Internet topology, like its high degree of clustering and its
robustness.
In this work, we study the modular structure of the Internet router-level
graph in order to assess to what extent the Autonomous Systems satisfy some of
the known notions of community structure. We show that the modular structure of
the Internet is much richer than what can be captured by the current community
detection methods, which are severely affected by resolution limits and by the
heterogeneity of the Autonomous Systems. Here we overcome this issue by using a
multiresolution detection algorithm combined with a small sample of nodes. We
also discuss recent work on community structure in the light of our results
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
Z-score-based modularity for community detection in networks
Identifying community structure in networks is an issue of particular
interest in network science. The modularity introduced by Newman and Girvan
[Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for
community detection in networks. In this study, we identify a problem in the
concept of modularity and suggest a solution to overcome this problem.
Specifically, we obtain a new quality function for community detection. We
refer to the function as Z-modularity because it measures the Z-score of a
given division with respect to the fraction of the number of edges within
communities. Our theoretical analysis shows that Z-modularity mitigates the
resolution limit of the original modularity in certain cases. Computational
experiments using both artificial networks and well-known real-world networks
demonstrate the validity and reliability of the proposed quality function.Comment: 8 pages, 10 figure
Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets
AbstractâThis paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective timeâspace adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index TermsâElectromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I
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Discovering Communities through Friendship
We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closestâfriendship between nodes in the network using the recently proposed Generalized Erds Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a systemâsize resolution limit. Our closestâfriend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multiâlevel structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as realâworld networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.Engineering and Applied SciencesPhysic
Exploratory data analysis using network based techniques
The aim of this document is to present the work done during the development
of my master thesis. The work belongs to the field of complex networks, more
concretely to the detection of communities in complex networks. Chapter 1 will
be an introduction of the basic concepts and motivations of this work, mainly
clarifying the fields of exploratory data analysis, data clustering and complex
networks. As all the work is about the finding of communities in complex networks,
Chapter 2 is devoted to explain the concepts of mesoscopic structure of
networks and its importance in the analysis of real networks, along with the explanations
of some of the most well-known techniques to perform this analysis.
All the progress done during the master thesis relies on a method for detecting
communities developed in the past years by the research group I belong to. This
method is known as the AFG algorithm, named after the three authors Arenas,
FernĂĄndez and GĂłmez, and it is explained in section 2.5.2 with special emphasis.
The work that I have developed is composed of two separate problems: the first
one consists in designing an application to make possible the use of the AFG
community detection method to perform data clustering over real world multidimensional
datasets, which is explained in Chapter 3. The second work consists in
improving the AFG method to make possible the detection of communities even
when the difference of sizes of the communities make their detection impossible
for other community detection algorithms, which can be found in Chapter 4.
Chapter 5 contains the conclusions and the future lines of research derived from
the present work, and in the Appendix there is a list of publications that sustain
the contents presented in this document
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
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