126,562 research outputs found
The diameter of the world wide web
Despite its increasing role in communication, the world wide web remains the
least controlled medium: any individual or institution can create websites with
unrestricted number of documents and links. While great efforts are made to map
and characterize the Internet's infrastructure, little is known about the
topology of the web. Here we take a first step to fill this gap: we use local
connectivity measurements to construct a topological model of the world wide
web, allowing us to explore and characterize its large scale properties.Comment: 5 pages, 1 figure, updated with most recent results on the size of
the ww
Deterministic Small-World Networks
Many real life networks, such as the World Wide Web, transportation systems,
biological or social networks, achieve both a strong local clustering (nodes
have many mutual neighbors) and a small diameter (maximum distance between any
two nodes). These networks have been characterized as small-world networks and
modeled by the addition of randomness to regular structures. We show that
small-world networks can be constructed in a deterministic way. This exact
approach permits a direct calculation of relevant network parameters allowing
their immediate contrast with real-world networks and avoiding complex computer
simulations.Comment: 6 pages, 1 figur
Optimal Scale-Free Small-World Graphs with Minimum Scaling of Cover Time
The cover time of random walks on a graph has found wide practical
applications in different fields of computer science, such as crawling and
searching on the World Wide Web and query processing in sensor networks, with
the application effects dependent on the behavior of cover time: the smaller
the cover time, the better the application performance. It was proved that over
all graphs with nodes, complete graphs have the minimum cover time . However, complete graphs cannot mimic real-world networks with small
average degree and scale-free small-world properties, for which the cover time
has not been examined carefully, and its behavior is still not well understood.
In this paper, we first experimentally evaluate the cover time for various
real-world networks with scale-free small-world properties, which scales as
. To better understand the behavior of the cover time for real-world
networks, we then study the cover time of three scale-free small-world model
networks by using the connection between cover time and resistance diameter.
For all the three networks, their cover time also behaves as . This
work indicates that sparse networks with scale-free and small-world topology
are favorable architectures with optimal scaling of cover time. Our results
deepen understanding the behavior of cover time in real-world networks with
scale-free small-world structure, and have potential implications in the design
of efficient algorithms related to cover time
Self-similarity of complex networks
Complex networks have been studied extensively due to their relevance to many
real systems as diverse as the World-Wide-Web (WWW), the Internet, energy
landscapes, biological and social networks
\cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real
networks are called ``scale-free'' because they show a power-law distribution
of the number of links per node \cite{ab-review,barabasi1999,faloutsos}.
However, it is widely believed that complex networks are not {\it length-scale}
invariant or self-similar. This conclusion originates from the ``small-world''
property of these networks, which implies that the number of nodes increases
exponentially with the ``diameter'' of the network
\cite{erdos,bollobas,milgram,watts}, rather than the power-law relation
expected for a self-similar structure. Nevertheless, here we present a novel
approach to the analysis of such networks, revealing that their structure is
indeed self-similar. This result is achieved by the application of a
renormalization procedure which coarse-grains the system into boxes containing
nodes within a given "size". Concurrently, we identify a power-law relation
between the number of boxes needed to cover the network and the size of the box
defining a finite self-similar exponent. These fundamental properties, which
are shown for the WWW, social, cellular and protein-protein interaction
networks, help to understand the emergence of the scale-free property in
complex networks. They suggest a common self-organization dynamics of diverse
networks at different scales into a critical state and in turn bring together
previously unrelated fields: the statistical physics of complex networks with
renormalization group, fractals and critical phenomena.Comment: 28 pages, 12 figures, more informations at http://www.jamlab.or
Detonation Database
Welcome to the GALCIT Explosion Dynamics Laboratory Detonation Database. The goal of this project is to compile, catalog and present experimental data on gaseous detonations. These data currently include cell width, critical tube diameter, initiation energy, and minimum tube diameter. They are formatted in tables and summary graphs, with citations to the original references. A printed version and a World Wide Web version have been prepared. The purpose of this database is to facilitate explosion hazards evaluations and comparisons with numerical simulations of detonation behavior
Potential Networks, Contagious Communities, and Understanding Social Network Structure
In this paper we study how the network of agents adopting a particular
technology relates to the structure of the underlying network over which the
technology adoption spreads. We develop a model and show that the network of
agents adopting a particular technology may have characteristics that differ
significantly from the social network of agents over which the technology
spreads. For example, the network induced by a cascade may have a heavy-tailed
degree distribution even if the original network does not.
This provides evidence that online social networks created by technology
adoption over an underlying social network may look fundamentally different
from social networks and indicates that using data from many online social
networks may mislead us if we try to use it to directly infer the structure of
social networks. Our results provide an alternate explanation for certain
properties repeatedly observed in data sets, for example: heavy-tailed degree
distribution, network densification, shrinking diameter, and network community
profile. These properties could be caused by a sort of `sampling bias' rather
than by attributes of the underlying social structure. By generating networks
using cascades over traditional network models that do not themselves contain
these properties, we can nevertheless reliably produce networks that contain
all these properties.
An opportunity for interesting future research is developing new methods that
correctly infer underlying network structure from data about a network that is
generated via a cascade spread over the underlying network.Comment: To Appear in Proceedings of the 22nd International World Wide Web
Conference(WWW 2013
Let Your CyberAlter Ego Share Information and Manage Spam
Almost all of us have multiple cyberspace identities, and these {\em
cyber}alter egos are networked together to form a vast cyberspace social
network. This network is distinct from the world-wide-web (WWW), which is being
queried and mined to the tune of billions of dollars everyday, and until
recently, has gone largely unexplored. Empirically, the cyberspace social
networks have been found to possess many of the same complex features that
characterize its real counterparts, including scale-free degree distributions,
low diameter, and extensive connectivity. We show that these topological
features make the latent networks particularly suitable for explorations and
management via local-only messaging protocols. {\em Cyber}alter egos can
communicate via their direct links (i.e., using only their own address books)
and set up a highly decentralized and scalable message passing network that can
allow large-scale sharing of information and data. As one particular example of
such collaborative systems, we provide a design of a spam filtering system, and
our large-scale simulations show that the system achieves a spam detection rate
close to 100%, while the false positive rate is kept around zero. This system
has several advantages over other recent proposals (i) It uses an already
existing network, created by the same social dynamics that govern our daily
lives, and no dedicated peer-to-peer (P2P) systems or centralized server-based
systems need be constructed; (ii) It utilizes a percolation search algorithm
that makes the query-generated traffic scalable; (iii) The network has a built
in trust system (just as in social networks) that can be used to thwart
malicious attacks; iv) It can be implemented right now as a plugin to popular
email programs, such as MS Outlook, Eudora, and Sendmail.Comment: 13 pages, 10 figure
Error and attack tolerance of complex networks
Many complex systems, such as communication networks, display a surprising
degree of robustness: while key components regularly malfunction, local
failures rarely lead to the loss of the global information-carrying ability of
the network. The stability of these complex systems is often attributed to the
redundant wiring of the functional web defined by the systems' components. In
this paper we demonstrate that error tolerance is not shared by all redundant
systems, but it is displayed only by a class of inhomogeneously wired networks,
called scale-free networks. We find that scale-free networks, describing a
number of systems, such as the World Wide Web, Internet, social networks or a
cell, display an unexpected degree of robustness, the ability of their nodes to
communicate being unaffected by even unrealistically high failure rates.
However, error tolerance comes at a high price: these networks are extremely
vulnerable to attacks, i.e. to the selection and removal of a few nodes that
play the most important role in assuring the network's connectivity.Comment: 14 pages, 4 figures, Late
Four Degrees of Separation, Really
We recently measured the average distance of users in the Facebook graph,
spurring comments in the scientific community as well as in the general press
("Four Degrees of Separation"). A number of interesting criticisms have been
made about the meaningfulness, methods and consequences of the experiment we
performed. In this paper we want to discuss some methodological aspects that we
deem important to underline in the form of answers to the questions we have
read in newspapers, magazines, blogs, or heard from colleagues. We indulge in
some reflections on the actual meaning of "average distance" and make a number
of side observations showing that, yes, 3.74 "degrees of separation" are really
few
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