762 research outputs found
Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
Many complex networks display a mesoscopic structure with groups of nodes
sharing many links with the other nodes in their group and comparatively few
with nodes of different groups. This feature is known as community structure
and encodes precious information about the organization and the function of the
nodes. Many algorithms have been proposed but it is not yet clear how they
should be tested. Recently we have proposed a general class of undirected and
unweighted benchmark graphs, with heterogenous distributions of node degree and
community size. An increasing attention has been recently devoted to develop
algorithms able to consider the direction and the weight of the links, which
require suitable benchmark graphs for testing. In this paper we extend the
basic ideas behind our previous benchmark to generate directed and weighted
networks with built-in community structure. We also consider the possibility
that nodes belong to more communities, a feature occurring in real systems,
like, e. g., social networks. As a practical application, we show how
modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E.
The code to create the benchmark graphs can be freely downloaded from
http://santo.fortunato.googlepages.com/inthepress
Optimal map of the modular structure of complex networks
Modular structure is pervasive in many complex networks of interactions
observed in natural, social and technological sciences. Its study sheds light
on the relation between the structure and function of complex systems.
Generally speaking, modules are islands of highly connected nodes separated by
a relatively small number of links. Every module can have contributions of
links from any node in the network. The challenge is to disentangle these
contributions to understand how the modular structure is built. The main
problem is that the analysis of a certain partition into modules involves, in
principle, as many data as number of modules times number of nodes. To confront
this challenge, here we first define the contribution matrix, the mathematical
object containing all the information about the partition of interest, and
after, we use a Truncated Singular Value Decomposition to extract the best
representation of this matrix in a plane. The analysis of this projection allow
us to scrutinize the skeleton of the modular structure, revealing the structure
of individual modules and their interrelations.Comment: 21 pages, 10 figure
Local multiresolution order in community detection
Community detection algorithms attempt to find the best clusters of nodes in
an arbitrary complex network. Multi-scale ("multiresolution") community
detection extends the problem to identify the best network scale(s) for these
clusters. The latter task is generally accomplished by analyzing community
stability simultaneously for all clusters in the network. In the current work,
we extend this general approach to define local multiresolution methods, which
enable the extraction of well-defined local communities even if the global
community structure is vaguely defined in an average sense. Toward this end, we
propose measures analogous to variation of information and normalized mutual
information that are used to quantitatively identify the best resolution(s) at
the community level based on correlations between clusters in
independently-solved systems. We demonstrate our method on two constructed
networks as well as a real network and draw inferences about local community
strength. Our approach is independent of the applied community detection
algorithm save for the inherent requirement that the method be able to identify
communities across different network scales, with appropriate changes to
account for how different resolutions are evaluated or defined in a particular
community detection method. It should, in principle, easily adapt to
alternative community comparison measures.Comment: 19 pages, 11 figure
Partitioning and modularity of graphs with arbitrary degree distribution
We solve the graph bi-partitioning problem in dense graphs with arbitrary
degree distribution using the replica method. We find the cut-size to scale
universally with . In contrast, earlier results studying the problem in
graphs with a Poissonian degree distribution had found a scaling with ^1/2
[Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also
generalize to the problem of q-partitioning. They can be used to find the
expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random
graphs and allow for the assessment of statistical significance of the output
of community detection algorithms.Comment: Revised version including new plots and improved discussion of some
mathematical detail
Modular synchronization in complex networks with a gauge Kuramoto model
We modify the Kuramoto model for synchronization on complex networks by
introducing a gauge term that depends on the edge betweenness centrality (BC).
The gauge term introduces additional phase difference between two vertices from
0 to as the BC on the edge between them increases from the minimum to the
maximum in the network. When the network has a modular structure, the model
generates the phase synchronization within each module, however, not over the
entire system. Based on this feature, we can distinguish modules in complex
networks, with relatively little computational time of , where
and are the number of vertices and edges in the system, respectively.
We also examine the synchronization of the modified Kuramoto model and compare
it with that of the original Kuramoto model in several complex networks.Comment: 10 pages, 7 figure
Outlier Edge Detection Using Random Graph Generation Models and Applications
Outliers are samples that are generated by different mechanisms from other
normal data samples. Graphs, in particular social network graphs, may contain
nodes and edges that are made by scammers, malicious programs or mistakenly by
normal users. Detecting outlier nodes and edges is important for data mining
and graph analytics. However, previous research in the field has merely focused
on detecting outlier nodes. In this article, we study the properties of edges
and propose outlier edge detection algorithms using two random graph generation
models. We found that the edge-ego-network, which can be defined as the induced
graph that contains two end nodes of an edge, their neighboring nodes and the
edges that link these nodes, contains critical information to detect outlier
edges. We evaluated the proposed algorithms by injecting outlier edges into
some real-world graph data. Experiment results show that the proposed
algorithms can effectively detect outlier edges. In particular, the algorithm
based on the Preferential Attachment Random Graph Generation model consistently
gives good performance regardless of the test graph data. Further more, the
proposed algorithms are not limited in the area of outlier edge detection. We
demonstrate three different applications that benefit from the proposed
algorithms: 1) a preprocessing tool that improves the performance of graph
clustering algorithms; 2) an outlier node detection algorithm; and 3) a novel
noisy data clustering algorithm. These applications show the great potential of
the proposed outlier edge detection techniques.Comment: 14 pages, 5 figures, journal pape
Comparing community structure identification
We compare recent approaches to community structure identification in terms
of sensitivity and computational cost. The recently proposed modularity measure
is revisited and the performance of the methods as applied to ad hoc networks
with known community structure, is compared. We find that the most accurate
methods tend to be more computationally expensive, and that both aspects need
to be considered when choosing a method for practical purposes. The work is
intended as an introduction as well as a proposal for a standard benchmark test
of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as
appears in JSTA
Multiple Nuclear Polarization States in a Double Quantum Dot
We observe multiple stable states of nuclear polarization in a double quantum
dot under conditions of electron spin resonance. The stable states can be
understood within an elaborated theoretical rate equation model for the
polarization in each of the dots, in the limit of strong driving. This model
also captures unusual features of the data, such as fast switching and a
`wrong' sign of polarization. The results reported enable applications of this
polarization effect, including manipulation and control of nuclear fields.Comment: 5 pages, 4 figures, 7 pages supplementary materia
Community Structure in Congressional Cosponsorship Networks
We study the United States Congress by constructing networks between Members
of Congress based on the legislation that they cosponsor. Using the concept of
modularity, we identify the community structure of Congressmen, as connected
via sponsorship/cosponsorship of the same legislation, to investigate the
collaborative communities of legislators in both chambers of Congress. This
analysis yields an explicit and conceptually clear measure of political
polarization, demonstrating a sharp increase in partisan polarization which
preceded and then culminated in the 104th Congress (1995-1996), when
Republicans took control of both chambers. Although polarization has since
waned in the U.S. Senate, it remains at historically high levels in the House
of Representatives.Comment: 8 pages, 4 figures (some with multiple parts), to appear in Physica
A; additional background info and explanations added from last versio
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