283 research outputs found
Local modularity measure for network clusterizations
Many complex networks have an underlying modular structure, i.e., structural
subunits (communities or clusters) characterized by highly interconnected
nodes. The modularity has been introduced as a measure to assess the
quality of clusterizations. has a global view, while in many real-world
networks clusters are linked mainly \emph{locally} among each other
(\emph{local cluster-connectivity}). Here, we introduce a new measure,
localized modularity , which reflects local cluster structure. Optimization
of and on the clusterization of two biological networks shows that the
localized modularity identifies more cohesive clusters, yielding a
complementary view of higher granularity.Comment: 5 pages, 4 figures, RevTex4; Changed conten
Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule
A spatial scale-free network is introduced and studied whose motivation has
been originated in the growing Internet as well as the Airport networks. We
argue that in these real-world networks a new node necessarily selects one of
its neighbouring local nodes for connection and is not controlled by the
preferential attachment as in the Barab\'asi-Albert (BA) model. This
observation has been mimicked in our model where the nodes pop-up at randomly
located positions in the Euclidean space and are connected to one end of the
nearest link. In spite of this crucial difference it is observed that the
leading behaviour of our network is like the BA model. Defining link weight as
an algebraic power of its Euclidean length, the weight distribution and the
non-linear dependence of the nodal strength on the degree are analytically
calculated. It is claimed that a power law decay of the link weights with time
ensures such a non-linear behavior. Switching off the Euclidean space from the
same model yields a much simpler definition of the Barab\'asi-Albert model
where numerical effort grows linearly with .Comment: 6 pages, 6 figure
Phase transition in a directed traffic flow network
The generic feature of traffic in a network of flowing electronic data
packets is a phase transition from a stationary free-flow phase to a
continuously growing congested non-stationary phase. In the most simple network
of directed oriented square lattice we have been able to observe all crucial
features of such flow systems having non-trivial critical behavior near the
critical point of transition. The network here is in the shape of a square
lattice and data packets are randomly posted with a rate at one side of
the lattice. Each packet executes a directed diffusive motion towards the
opposite boundary where it is delivered. Packets accumulated at a particular
node form a queue and a maximum of such packets randomly jump out of this
node at every time step to its neighbors on a first-in-first-out (FIFO) basis.
The phase transition occurs at . The distribution of travel times
through the system is found to have a log-normal behavior and the
power-spectrum of the load time-series shows like noise similar to the
scenario of Internet traffic.Comment: Six pages, seven figure
Problems with Fitting to the Power-Law Distribution
This short communication uses a simple experiment to show that fitting to a
power law distribution by using graphical methods based on linear fit on the
log-log scale is biased and inaccurate. It shows that using maximum likelihood
estimation (MLE) is far more robust. Finally, it presents a new table for
performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to
power-law distributions in which the power-law exponent is estimated using MLE.
The techniques presented here will advance the application of complex network
theory by allowing reliable estimation of power-law models from data and
further allowing quantitative assessment of goodness-of-fit of proposed
power-law models to empirical data.Comment: 4 pages, 1 figure, 2 table
Condition numbers and scale free graphs
In this work we study the condition number of the least square matrix
corresponding to scale free networks. We compute a theoretical lower bound of
the condition number which proves that they are ill conditioned. Also, we
analyze several matrices from networks generated with the linear preferential
attachment model showing that it is very difficult to compute the power law
exponent by the least square method due to the severe lost of accuracy expected
from the corresponding condition numbers.Comment: Submitted to EP
Optimization of Robustness of Complex Networks
Networks with a given degree distribution may be very resilient to one type
of failure or attack but not to another. The goal of this work is to determine
network design guidelines which maximize the robustness of networks to both
random failure and intentional attack while keeping the cost of the network
(which we take to be the average number of links per node) constant. We find
optimal parameters for: (i) scale free networks having degree distributions
with a single power-law regime, (ii) networks having degree distributions with
two power-law regimes, and (iii) networks described by degree distributions
containing two peaks. Of these various kinds of distributions we find that the
optimal network design is one in which all but one of the nodes have the same
degree, (close to the average number of links per node), and one node is
of very large degree, , where is the number of nodes in
the network.Comment: Accepted for publication in European Physical Journal
Quantitative description and modeling of real networks
In this letter we present data analysis and modeling of two particular cases
of study in the field of growing networks. We analyze WWW data set and
authorship collaboration networks in order to check the presence of correlation
in the data. The results are reproduced with a pretty good agreement through a
suitable modification of the standard AB model of network growth. In
particular, intrinsic relevance of sites plays a role in determining the future
degree of the vertex.Comment: 4 pages, 3 figure
Local versus Global Knowledge in the Barabasi-Albert scale-free network model
The scale-free model of Barabasi and Albert gave rise to a burst of activity
in the field of complex networks. In this paper, we revisit one of the main
assumptions of the model, the preferential attachment rule. We study a model in
which the PA rule is applied to a neighborhood of newly created nodes and thus
no global knowledge of the network is assumed. We numerically show that global
properties of the BA model such as the connectivity distribution and the
average shortest path length are quite robust when there is some degree of
local knowledge. In contrast, other properties such as the clustering
coefficient and degree-degree correlations differ and approach the values
measured for real-world networks.Comment: Revtex format. Final version appeared in PR
From Cooperative Scans to Predictive Buffer Management
In analytical applications, database systems often need to sustain workloads
with multiple concurrent scans hitting the same table. The Cooperative Scans
(CScans) framework, which introduces an Active Buffer Manager (ABM) component
into the database architecture, has been the most effective and elaborate
response to this problem, and was initially developed in the X100 research
prototype. We now report on the the experiences of integrating Cooperative
Scans into its industrial-strength successor, the Vectorwise database product.
During this implementation we invented a simpler optimization of concurrent
scan buffer management, called Predictive Buffer Management (PBM). PBM is based
on the observation that in a workload with long-running scans, the buffer
manager has quite a bit of information on the workload in the immediate future,
such that an approximation of the ideal OPT algorithm becomes feasible. In the
evaluation on both synthetic benchmarks as well as a TPC-H throughput run we
compare the benefits of naive buffer management (LRU) versus CScans, PBM and
OPT; showing that PBM achieves benefits close to Cooperative Scans, while
incurring much lower architectural impact.Comment: VLDB201
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