29,497 research outputs found
Laplacian Dynamics and Multiscale Modular Structure in Networks
Most methods proposed to uncover communities in complex networks rely on
their structural properties. Here we introduce the stability of a network
partition, a measure of its quality defined in terms of the statistical
properties of a dynamical process taking place on the graph. The time-scale of
the process acts as an intrinsic parameter that uncovers community structures
at different resolutions. The stability extends and unifies standard notions
for community detection: modularity and spectral partitioning can be seen as
limiting cases of our dynamic measure. Similarly, recently proposed
multi-resolution methods correspond to linearisations of the stability at short
times. The connection between community detection and Laplacian dynamics
enables us to establish dynamically motivated stability measures linked to
distinct null models. We apply our method to find multi-scale partitions for
different networks and show that the stability can be computed efficiently for
large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and
the generalisation of stability to directed network
Multi-scale Modularity in Complex Networks
We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure
Modularity and the spread of perturbations in complex dynamical systems
We propose a method to decompose dynamical systems based on the idea that
modules constrain the spread of perturbations. We find partitions of system
variables that maximize 'perturbation modularity', defined as the
autocovariance of coarse-grained perturbed trajectories. The measure
effectively separates the fast intramodular from the slow intermodular dynamics
of perturbation spreading (in this respect, it is a generalization of the
'Markov stability' method of network community detection). Our approach
captures variation of modular organization across different system states, time
scales, and in response to different kinds of perturbations: aspects of
modularity which are all relevant to real-world dynamical systems. It offers a
principled alternative to detecting communities in networks of statistical
dependencies between system variables (e.g., 'relevance networks' or
'functional networks'). Using coupled logistic maps, we demonstrate that the
method uncovers hierarchical modular organization planted in a system's
coupling matrix. Additionally, in homogeneously-coupled map lattices, it
identifies the presence of self-organized modularity that depends on the
initial state, dynamical parameters, and type of perturbations. Our approach
offers a powerful tool for exploring the modular organization of complex
dynamical systems
Dynamic reconfiguration of human brain networks during learning
Human learning is a complex phenomenon requiring flexibility to adapt
existing brain function and precision in selecting new neurophysiological
activities to drive desired behavior. These two attributes -- flexibility and
selection -- must operate over multiple temporal scales as performance of a
skill changes from being slow and challenging to being fast and automatic. Such
selective adaptability is naturally provided by modular structure, which plays
a critical role in evolution, development, and optimal network function. Using
functional connectivity measurements of brain activity acquired from initial
training through mastery of a simple motor skill, we explore the role of
modularity in human learning by identifying dynamic changes of modular
organization spanning multiple temporal scales. Our results indicate that
flexibility, which we measure by the allegiance of nodes to modules, in one
experimental session predicts the relative amount of learning in a future
session. We also develop a general statistical framework for the identification
of modular architectures in evolving systems, which is broadly applicable to
disciplines where network adaptability is crucial to the understanding of
system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4
figures, 3 table
An information-theoretic framework for resolving community structure in complex networks
To understand the structure of a large-scale biological, social, or
technological network, it can be helpful to decompose the network into smaller
subunits or modules. In this article, we develop an information-theoretic
foundation for the concept of modularity in networks. We identify the modules
of which the network is composed by finding an optimal compression of its
topology, capitalizing on regularities in its structure. We explain the
advantages of this approach and illustrate them by partitioning a number of
real-world and model networks.Comment: 5 pages, 4 figure
Temporal stability of network partitions
We present a method to find the best temporal partition at any time-scale and
rank the relevance of partitions found at different time-scales. This method is
based on random walkers coevolving with the network and as such constitutes a
generalization of partition stability to the case of temporal networks. We show
that, when applied to a toy model and real datasets, temporal stability
uncovers structures that are persistent over meaningful time-scales as well as
important isolated events, making it an effective tool to study both abrupt
changes and gradual evolution of a network mesoscopic structures.Comment: 15 pages, 12 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 structure in real-world networks from a non-parametrical synchronization-based dynamical approach
This work analyzes the problem of community structure in real-world networks
based on the synchronization of nonidentical coupled chaotic R\"{o}ssler
oscillators each one characterized by a defined natural frequency, and coupled
according to a predefined network topology. The interaction scheme contemplates
an uniformly increasing coupling force to simulate a society in which the
association between the agents grows in time. To enhance the stability of the
correlated states that could emerge from the synchronization process, we
propose a parameterless mechanism that adapts the characteristic frequencies of
coupled oscillators according to a dynamic connectivity matrix deduced from
correlated data. We show that the characteristic frequency vector that results
from the adaptation mechanism reveals the underlying community structure
present in the network.Comment: 21 pages, 7 figures; Chaos, Solitons & Fractals (2012
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