537 research outputs found
Sustainable growth in complex networks
Based on the empirical analysis of the dependency network in 18 Java
projects, we develop a novel model of network growth which considers both: an
attachment mechanism and the addition of new nodes with a heterogeneous
distribution of their initial degree, . Empirically we find that the
cumulative degree distributions of initial degrees and of the final network,
follow power-law behaviors: , and
, respectively. For the total number of links as a
function of the network size, we find empirically ,
where is (at the beginning of the network evolution) between 1.25 and
2, while converging to for large . This indicates a transition from
a growth regime with increasing network density towards a sustainable regime,
which revents a collapse because of ever increasing dependencies. Our
theoretical framework is able to predict relations between the exponents
, , , which also link issues of software engineering and
developer activity. These relations are verified by means of computer
simulations and empirical investigations. They indicate that the growth of real
Open Source Software networks occurs on the edge between two regimes, which are
either dominated by the initial degree distribution of added nodes, or by the
preferential attachment mechanism. Hence, the heterogeneous degree distribution
of newly added nodes, found empirically, is essential to describe the laws of
sustainable growth in networks.Comment: 5 pages, 2 figures, 1 tabl
Accelerated growth in outgoing links in evolving networks: deterministic vs. stochastic picture
In several real-world networks like the Internet, WWW etc., the number of
links grow in time in a non-linear fashion. We consider growing networks in
which the number of outgoing links is a non-linear function of time but new
links between older nodes are forbidden. The attachments are made using a
preferential attachment scheme. In the deterministic picture, the number of
outgoing links at any time is taken as where is
the number of nodes present at that time. The continuum theory predicts a power
law decay of the degree distribution: , while the degree of the node introduced at time is given by
when the
network is evolved till time . Numerical results show a growth in the degree
distribution for small values at any non-zero . In the stochastic
picture, is a random variable. As long as is time-dependent, e.g.,
when follows a distribution . The behaviour
of changes significantly as is varied: for , the
network has a scale-free distribution belonging to the BA class as predicted by
the mean field theory, for smaller values of it shows different
behaviour. Characteristic features of the clustering coefficients in both
models have also been discussed.Comment: Revised text, references added, to be published in PR
Revisit Behavior in Social Media: The Phoenix-R Model and Discoveries
How many listens will an artist receive on a online radio? How about plays on
a YouTube video? How many of these visits are new or returning users? Modeling
and mining popularity dynamics of social activity has important implications
for researchers, content creators and providers. We here investigate the effect
of revisits (successive visits from a single user) on content popularity. Using
four datasets of social activity, with up to tens of millions media objects
(e.g., YouTube videos, Twitter hashtags or LastFM artists), we show the effect
of revisits in the popularity evolution of such objects. Secondly, we propose
the Phoenix-R model which captures the popularity dynamics of individual
objects. Phoenix-R has the desired properties of being: (1) parsimonious, being
based on the minimum description length principle, and achieving lower root
mean squared error than state-of-the-art baselines; (2) applicable, the model
is effective for predicting future popularity values of objects.Comment: To appear on European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases 201
Extreme self-organization in networks constructed from gene expression data
We study networks constructed from gene expression data obtained from many
types of cancers. The networks are constructed by connecting vertices that
belong to each others' list of K-nearest-neighbors, with K being an a priori
selected non-negative integer. We introduce an order parameter for
characterizing the homogeneity of the networks. On minimizing the order
parameter with respect to K, degree distribution of the networks shows
power-law behavior in the tails with an exponent of unity. Analysis of the
eigenvalue spectrum of the networks confirms the presence of the power-law and
small-world behavior. We discuss the significance of these findings in the
context of evolutionary biological processes.Comment: 4 pages including 3 eps figures, revtex. Revisions as in published
versio
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
Scaling of load in communications networks
We show that the load at each node in a preferential attachment network
scales as a power of the degree of the node. For a network whose degree
distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with
eta = gamma - 1, implying that the probability distribution for the load is
p(l) ~ 1/l^2 independent of gamma. The results are obtained through scaling
arguments supported by finite size scaling studies. They contradict earlier
claims, but are in agreement with the exact solution for the special case of
tree graphs. Results are also presented for real communications networks at the
IP layer, using the latest available data. Our analysis of the data shows
relatively poor power-law degree distributions as compared to the scaling of
the load versus degree. This emphasizes the importance of the load in network
analysis.Comment: 4 pages, 5 figure
A dissemination strategy for immunizing scale-free networks
We consider the problem of distributing a vaccine for immunizing a scale-free
network against a given virus or worm. We introduce a new method, based on
vaccine dissemination, that seems to reflect more accurately what is expected
to occur in real-world networks. Also, since the dissemination is performed
using only local information, the method can be easily employed in practice.
Using a random-graph framework, we analyze our method both mathematically and
by means of simulations. We demonstrate its efficacy regarding the trade-off
between the expected number of nodes that receive the vaccine and the network's
resulting vulnerability to develop an epidemic as the virus or worm attempts to
infect one of its nodes. For some scenarios, the new method is seen to render
the network practically invulnerable to attacks while requiring only a small
fraction of the nodes to receive the vaccine
A New Methodology for Generalizing Unweighted Network Measures
Several important complex network measures that helped discovering common
patterns across real-world networks ignore edge weights, an important
information in real-world networks. We propose a new methodology for
generalizing measures of unweighted networks through a generalization of the
cardinality concept of a set of weights. The key observation here is that many
measures of unweighted networks use the cardinality (the size) of some subset
of edges in their computation. For example, the node degree is the number of
edges incident to a node. We define the effective cardinality, a new metric
that quantifies how many edges are effectively being used, assuming that an
edge's weight reflects the amount of interaction across that edge. We prove
that a generalized measure, using our method, reduces to the original
unweighted measure if there is no disparity between weights, which ensures that
the laws that govern the original unweighted measure will also govern the
generalized measure when the weights are equal. We also prove that our
generalization ensures a partial ordering (among sets of weighted edges) that
is consistent with the original unweighted measure, unlike previously developed
generalizations. We illustrate the applicability of our method by generalizing
four unweighted network measures. As a case study, we analyze four real-world
weighted networks using our generalized degree and clustering coefficient. The
analysis shows that the generalized degree distribution is consistent with the
power-law hypothesis but with steeper decline and that there is a common
pattern governing the ratio between the generalized degree and the traditional
degree. The analysis also shows that nodes with more uniform weights tend to
cluster with nodes that also have more uniform weights among themselves.Comment: 23 pages, 10 figure
Exploring complex networks by walking on them
We carry out a comparative study on the problem for a walker searching on
several typical complex networks. The search efficiency is evaluated for
various strategies. Having no knowledge of the global properties of the
underlying networks and the optimal path between any two given nodes, it is
found that the best search strategy is the self-avoid random walk. The
preferentially self-avoid random walk does not help in improving the search
efficiency further. In return, topological information of the underlying
networks may be drawn by comparing the results of the different search
strategies.Comment: 5 pages, 5 figure
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
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