254 research outputs found
Improved spectral algorithm for the detection of network communities
We review and improve a recently introduced method for the detection of
communities in complex networks. This method combines spectral properties of
some matrices encoding the network topology, with well known hierarchical
clustering techniques, and the use of the modularity parameter to quantify the
goodness of any possible community subdivision. This provides one of the best
available methods for the detection of community structures in complex systems.Comment: 4 pages, 1 fugure; to appear in the Proceedings of the 8th Granada
Seminar - Computational and Statistical Physic
Network synchronization: Optimal and Pessimal Scale-Free Topologies
By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex
Networks 2007
The spectral dimension of random trees
We present a simple yet rigorous approach to the determination of the
spectral dimension of random trees, based on the study of the massless limit of
the Gaussian model on such trees. As a byproduct, we obtain evidence in favor
of a new scaling hypothesis for the Gaussian model on generic bounded graphs
and in favor of a previously conjectured exact relation between spectral and
connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section
I
Community detection in complex networks using Extremal Optimization
We propose a novel method to find the community structure in complex networks
based on an extremal optimization of the value of modularity. The method
outperforms the optimal modularity found by the existing algorithms in the
literature. We present the results of the algorithm for computer simulated and
real networks and compare them with other approaches. The efficiency and
accuracy of the method make it feasible to be used for the accurate
identification of community structure in large complex networks.Comment: 4 pages, 4 figure
Error Correction in Vergence Eye Movements: Evidence Supporting Hering’s Law
In pure symmetrical vergence eye movements, a fusion initiating component quickly brings the eyes close to the desired position. A small error usually remains after this response which must be corrected to attain the small final vergence error (i.e., fixation disparity). Error correction will usually involve both version and version movements so possible mechanisms include: small saccades, smooth pursuit, symmetrical vergence, or some combination. Alternatively, an asymmetrical vergence or uniocular slow eye movement could be used to achieve the highly precise final position. Saccade-free late fusion sustaining components during the steady state to a symmetrical vergence step stimulus are analyzed using independent component analysis. Results suggest that fine correction is most likely the product of closely coordinated version and vergence components
Network evolution towards optimal dynamical performance
Understanding the mutual interdependence between the behavior of dynamical
processes on networks and the underlying topologies promises new insight for a
large class of empirical networks. We present a generic approach to investigate
this relationship which is applicable to a wide class of dynamics, namely to
evolve networks using a performance measure based on the whole spectrum of the
dynamics' time evolution operator. As an example, we consider the graph
Laplacian describing diffusion processes, and we evolve the network structure
such that a given sub-diffusive behavior emerges.Comment: 5 pages, 4 figure
Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
We report on some recent developments in the search for optimal network
topologies. First we review some basic concepts on spectral graph theory,
including adjacency and Laplacian matrices, and paying special attention to the
topological implications of having large spectral gaps. We also introduce
related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we
discuss two different dynamical feautures of networks: synchronizability and
flow of random walkers and so that they are optimized if the corresponding
Laplacian matrix have a large spectral gap. From this, we show, by developing a
numerical optimization algorithm that maximum synchronizability and fast random
walk spreading are obtained for a particular type of extremely homogeneous
regular networks, with long loops and poor modular structure, that we call
entangled networks. These turn out to be related to Ramanujan and Cage graphs.
We argue also that these graphs are very good finite-size approximations to
Bethe lattices, and provide almost or almost optimal solutions to many other
problems as, for instance, searchability in the presence of congestion or
performance of neural networks. Finally, we study how these results are
modified when studying dynamical processes controlled by a normalized (weighted
and directed) dynamics; much more heterogeneous graphs are optimal in this
case. Finally, a critical discussion of the limitations and possible extensions
of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted
for pub. in JSTA
A New Comparative Definition of Community and Corresponding Identifying Algorithm
In this paper, a new comparative definition for community in networks is
proposed and the corresponding detecting algorithm is given. A community is
defined as a set of nodes, which satisfy that each node's degree inside the
community should not be smaller than the node's degree toward any other
community. In the algorithm, the attractive force of a community to a node is
defined as the connections between them. Then employing attractive force based
self-organizing process, without any extra parameter, the best communities can
be detected. Several artificial and real-world networks, including Zachary
Karate club network and College football network are analyzed. The algorithm
works well in detecting communities and it also gives a nice description for
network division and group formation.Comment: 11 pages, 4 fihure
Entangled networks, synchronization, and optimal network topology
A new family of graphs, {\it entangled networks}, with optimal properties in
many respects, is introduced. By definition, their topology is such that
optimizes synchronizability for many dynamical processes. These networks are
shown to have an extremely homogeneous structure: degree, node-distance,
betweenness, and loop distributions are all very narrow. Also, they are
characterized by a very interwoven (entangled) structure with short average
distances, large loops, and no well-defined community-structure. This family of
nets exhibits an excellent performance with respect to other flow properties
such as robustness against errors and attacks, minimal first-passage time of
random walks, efficient communication, etc. These remarkable features convert
entangled networks in a useful concept, optimal or almost-optimal in many
senses, and with plenty of potential applications computer science or
neuroscience.Comment: Slightly modified version, as accepted in Phys. Rev. Let
- …