35 research outputs found
On the universality of the scaling of fluctuations in traffic on complex networks
We study the scaling of fluctuations with the mean of traffic in complex
networks using a model where the arrival and departure of "packets" follow
exponential distributions, and the processing capability of nodes is either
unlimited or finite. The model presents a wide variety of exponents between 1/2
and 1 for this scaling, revealing their dependence on the few parameters
considered, and questioning the existence of universality classes. We also
report the experimental scaling of the fluctuations in the Internet for the
Abilene backbone network. We found scaling exponents between 0.71 and 0.86 that
do not fit with the exponent 1/2 reported in the literature.Comment: 4 pages, 4 figure
Size reduction of complex networks preserving modularity
The ubiquity of modular structure in real-world complex networks is being the
focus of attention in many trials to understand the interplay between network
topology and functionality. The best approaches to the identification of
modular structure are based on the optimization of a quality function known as
modularity. However this optimization is a hard task provided that the
computational complexity of the problem is in the NP-hard class. Here we
propose an exact method for reducing the size of weighted (directed and
undirected) complex networks while maintaining invariant its modularity. This
size reduction allows the heuristic algorithms that optimize modularity for a
better exploration of the modularity landscape. We compare the modularity
obtained in several real complex-networks by using the Extremal Optimization
algorithm, before and after the size reduction, showing the improvement
obtained. We speculate that the proposed analytical size reduction could be
extended to an exact coarse graining of the network in the scope of real-space
renormalization.Comment: 14 pages, 2 figure
Enhance the Efficiency of Heuristic Algorithm for Maximizing Modularity Q
Modularity Q is an important function for identifying community structure in
complex networks. In this paper, we prove that the modularity maximization
problem is equivalent to a nonconvex quadratic programming problem. This result
provide us a simple way to improve the efficiency of heuristic algorithms for
maximizing modularity Q. Many numerical results demonstrate that it is very
effective.Comment: 9 pages, 3 figure
An evolving network model with community structure
Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties
Improved community structure detection using a modified fine tuning strategy
The community structure of a complex network can be determined by finding the
partitioning of its nodes that maximizes modularity. Many of the proposed
algorithms for doing this work by recursively bisecting the network. We show
that this unduely constrains their results, leading to a bias in the size of
the communities they find and limiting their effectivness. To solve this
problem, we propose adding a step to the existing algorithms that does not
increase the order of their computational complexity. We show that, if this
step is combined with a commonly used method, the identified constraint and
resulting bias are removed, and its ability to find the optimal partitioning is
improved. The effectiveness of this combined algorithm is also demonstrated by
using it on real-world example networks. For a number of these examples, it
achieves the best results of any known algorithm.Comment: 6 pages, 3 figures, 1 tabl
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
Who is the best player ever? A complex network analysis of the history of professional tennis
We consider all matches played by professional tennis players between 1968
and 2010, and, on the basis of this data set, construct a directed and weighted
network of contacts. The resulting graph shows complex features, typical of
many real networked systems studied in literature. We develop a diffusion
algorithm and apply it to the tennis contact network in order to rank
professional players. Jimmy Connors is identified as the best player of the
history of tennis according to our ranking procedure. We perform a complete
analysis by determining the best players on specific playing surfaces as well
as the best ones in each of the years covered by the data set. The results of
our technique are compared to those of two other well established methods. In
general, we observe that our ranking method performs better: it has a higher
predictive power and does not require the arbitrary introduction of external
criteria for the correct assessment of the quality of players. The present work
provides a novel evidence of the utility of tools and methods of network theory
in real applications.Comment: 10 pages, 4 figures, 4 table
Mesoscopic structure conditions the emergence of cooperation on social networks
We study the evolutionary Prisoner's Dilemma on two social networks obtained
from actual relational data. We find very different cooperation levels on each
of them that can not be easily understood in terms of global statistical
properties of both networks. We claim that the result can be understood at the
mesoscopic scale, by studying the community structure of the networks. We
explain the dependence of the cooperation level on the temptation parameter in
terms of the internal structure of the communities and their interconnections.
We then test our results on community-structured, specifically designed
artificial networks, finding perfect agreement with the observations in the
real networks. Our results support the conclusion that studies of evolutionary
games on model networks and their interpretation in terms of global properties
may not be sufficient to study specific, real social systems. In addition, the
community perspective may be helpful to interpret the origin and behavior of
existing networks as well as to design structures that show resilient
cooperative behavior.Comment: Largely improved version, includes an artificial network model that
fully confirms the explanation of the results in terms of inter- and
intra-community structur
Frustrated hierarchical synchronization and emergent complexity in the human connectome network
The spontaneous emergence of coherent behavior through synchronization plays a key role in neural function, and its anomalies often lie at the basis of pathologies. Here we employ a parsimonious (mesoscopic) approach to study analytically and computationally the synchronization (Kuramoto) dynamics on the actual human-brain connectome network. We elucidate the existence of a so-far-uncovered intermediate phase, placed between the standard synchronous and asynchronous phases, i.e. between order and disorder. This novel phase stems from the hierarchical modular organization of the connectome. Where one would expect a hierarchical synchronization process, we show that the interplay between structural bottlenecks and quenched intrinsic frequency heterogeneities at many different scales, gives rise to frustrated synchronization, metastability, and chimera-like states, resulting in a very rich and complex phenomenology. We uncover the origin of the dynamic freezing behind these features by using spectral graph theory and discuss how the emerging complex synchronization patterns relate to the need for the brain to access –in a robust though flexible way– a large variety of functional attractors and dynamical repertoires without ad hoc fine-tuning to a critical pointWe acknowledge financial support from J. de AndalucĂa, grant P09-FQM-4682 and we thank O. Sporns for providing us access to the human connectome data
Improving the Louvain Algorithm for Community Detection with Modularity Maximization
International audienc