176 research outputs found
Preferential attachment in the growth of social networks: the case of Wikipedia
We present an analysis of the statistical properties and growth of the free
on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks
between them as edges, we can represent this encyclopedia as a directed graph.
The topological properties of this graph are in close analogy with that of the
World Wide Web, despite the very different growth mechanism. In particular we
measure a scale--invariant distribution of the in-- and out-- degree and we are
able to reproduce these features by means of a simple statistical model. As a
major consequence, Wikipedia growth can be described by local rules such as the
preferential attachment mechanism, though users can act globally on the
network.Comment: 4 pages, 4 figures, revte
Finding instabilities in the community structure of complex networks
The problem of finding clusters in complex networks has been extensively
studied by mathematicians, computer scientists and, more recently, by
physicists. Many of the existing algorithms partition a network into clear
clusters, without overlap. We here introduce a method to identify the nodes
lying ``between clusters'' and that allows for a general measure of the
stability of the clusters. This is done by adding noise over the weights of the
edges of the network. Our method can in principle be applied with any
clustering algorithm, provided that it works on weighted networks. We present
several applications on real-world networks using the Markov Clustering
Algorithm (MCL).Comment: 4 pages, 5 figure
Analysis of weighted networks
The connections in many networks are not merely binary entities, either
present or not, but have associated weights that record their strengths
relative to one another. Recent studies of networks have, by and large, steered
clear of such weighted networks, which are often perceived as being harder to
analyze than their unweighted counterparts. Here we point out that weighted
networks can in many cases be analyzed using a simple mapping from a weighted
network to an unweighted multigraph, allowing us to apply standard techniques
for unweighted graphs to weighted ones as well. We give a number of examples of
the method, including an algorithm for detecting community structure in
weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure
Cliques and duplication-divergence network growth
A population of complete subgraphs or cliques in a network evolving via
duplication-divergence is considered. We find that a number of cliques of each
size scales linearly with the size of the network. We also derive a clique
population distribution that is in perfect agreement with both the simulation
results and the clique statistic of the protein-protein binding network of the
fruit fly. In addition, we show that such features as fat-tail degree
distribution, various rates of average degree growth and non-averaging,
revealed recently for only the particular case of a completely asymmetric
divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure
A Yule-Simon process with memory
The Yule-Simon model has been used as a tool to describe the growth of
diverse systems, acquiring a paradigmatic character in many fields of research.
Here we study a modified Yule-Simon model that takes into account the full
history of the system by means of an hyperbolic memory kernel. We show how the
memory kernel changes the properties of preferential attachment and provide an
approximate analytical solution for the frequency distribution density as well
as for the frequency-rank distribution.Comment: 7 pages, 5 figures; accepted for publication in Europhysics Letter
Two-dimensional ranking of Wikipedia articles
The Library of Babel, described by Jorge Luis Borges, stores an enormous
amount of information. The Library exists {\it ab aeterno}. Wikipedia, a free
online encyclopaedia, becomes a modern analogue of such a Library. Information
retrieval and ranking of Wikipedia articles become the challenge of modern
society. While PageRank highlights very well known nodes with many ingoing
links, CheiRank highlights very communicative nodes with many outgoing links.
In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we
analyze the properties of two-dimensional ranking of all Wikipedia English
articles and show that it gives their reliable classification with rich and
nontrivial features. Detailed studies are done for countries, universities,
personalities, physicists, chess players, Dow-Jones companies and other
categories.Comment: RevTex 9 pages, data, discussion added, more data at
http://www.quantware.ups-tlse.fr/QWLIB/2drankwikipedia
Inter-arrival times of message propagation on directed networks
One of the challenges in fighting cybercrime is to understand the dynamics of
message propagation on botnets, networks of infected computers used to send
viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We
map this problem to the propagation of multiple random walkers on directed
networks and we evaluate the inter-arrival time distribution between successive
walkers arriving at a target. We show that the temporal organization of this
process, which models information propagation on unstructured peer to peer
networks, has the same features as SPAM arriving to a single user. We study the
behavior of the message inter-arrival time distribution on three different
network topologies using two different rules for sending messages. In all
networks the propagation is not a pure Poisson process. It shows universal
features on Poissonian networks and a more complex behavior on scale free
networks. Results open the possibility to indirectly learn about the process of
sending messages on networks with unknown topologies, by studying inter-arrival
times at any node of the network.Comment: 9 pages, 12 figure
The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities
We consider the exact solutions of the supergravity theories in various
dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is
an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere
of an appropriate dimension. We show that, if the cosmological constant of
M_{d} is negative and the conformal Killing vector is space-like, then such
solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where
M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the
properties of the limiting solutions and find that M^{(0)}_{d} has 1/4
supersymmetry as well as a Virasoro symmetry. We also describe how the
pp-curvature singularity of M^{(0)}_{d} is resolved in the particular case of
the D6-branes of D=10 type IIA supergravity theory. This distinguished case
provides an interesting generalization of the plane waves in D=11 supergravity
theory and suggests a duality between the SU(2) gauged d=8 supergravity of
Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its
pp-wave boundary.Comment: 20 pages, LaTeX; typos corrected, journal versio
Self-organized network evolution coupled to extremal dynamics
The interplay between topology and dynamics in complex networks is a
fundamental but widely unexplored problem. Here, we study this phenomenon on a
prototype model in which the network is shaped by a dynamical variable. We
couple the dynamics of the Bak-Sneppen evolution model with the rules of the
so-called fitness network model for establishing the topology of a network;
each vertex is assigned a fitness, and the vertex with minimum fitness and its
neighbours are updated in each iteration. At the same time, the links between
the updated vertices and all other vertices are drawn anew with a
fitness-dependent connection probability. We show analytically and numerically
that the system self-organizes to a non-trivial state that differs from what is
obtained when the two processes are decoupled. A power-law decay of dynamical
and topological quantities above a threshold emerges spontaneously, as well as
a feedback between different dynamical regimes and the underlying correlation
and percolation properties of the network.Comment: Accepted version. Supplementary information at
http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm
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