45,741 research outputs found
The Internet AS-Level Topology: Three Data Sources and One Definitive Metric
We calculate an extensive set of characteristics for Internet AS topologies
extracted from the three data sources most frequently used by the research
community: traceroutes, BGP, and WHOIS. We discover that traceroute and BGP
topologies are similar to one another but differ substantially from the WHOIS
topology. Among the widely considered metrics, we find that the joint degree
distribution appears to fundamentally characterize Internet AS topologies as
well as narrowly define values for other important metrics. We discuss the
interplay between the specifics of the three data collection mechanisms and the
resulting topology views. In particular, we show how the data collection
peculiarities explain differences in the resulting joint degree distributions
of the respective topologies. Finally, we release to the community the input
topology datasets, along with the scripts and output of our calculations. This
supplement should enable researchers to validate their models against real data
and to make more informed selection of topology data sources for their specific
needs.Comment: This paper is a revised journal version of cs.NI/050803
A critical look at power law modelling of the Internet
This paper takes a critical look at the usefulness of power law models of the
Internet. The twin focuses of the paper are Internet traffic and topology
generation. The aim of the paper is twofold. Firstly it summarises the state of
the art in power law modelling particularly giving attention to existing open
research questions. Secondly it provides insight into the failings of such
models and where progress needs to be made for power law research to feed
through to actual improvements in network performance.Comment: To appear Computer Communication
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential
Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type
Large-scale topological and dynamical properties of Internet
We study the large-scale topological and dynamical properties of real
Internet maps at the autonomous system level, collected in a three years time
interval. We find that the connectivity structure of the Internet presents
average quantities and statistical distributions settled in a well-defined
stationary state. The large-scale properties are characterized by a scale-free
topology consistent with previous observations. Correlation functions and
clustering coefficients exhibit a remarkable structure due to the underlying
hierarchical organization of the Internet. The study of the Internet time
evolution shows a growth dynamics with aging features typical of recently
proposed growing network models. We compare the properties of growing network
models with the present real Internet data analysis.Comment: 13 pages, 15 eps figure
A Latent Parameter Node-Centric Model for Spatial Networks
Spatial networks, in which nodes and edges are embedded in space, play a
vital role in the study of complex systems. For example, many social networks
attach geo-location information to each user, allowing the study of not only
topological interactions between users, but spatial interactions as well. The
defining property of spatial networks is that edge distances are associated
with a cost, which may subtly influence the topology of the network. However,
the cost function over distance is rarely known, thus developing a model of
connections in spatial networks is a difficult task.
In this paper, we introduce a novel model for capturing the interaction
between spatial effects and network structure. Our approach represents a unique
combination of ideas from latent variable statistical models and spatial
network modeling. In contrast to previous work, we view the ability to form
long/short-distance connections to be dependent on the individual nodes
involved. For example, a node's specific surroundings (e.g. network structure
and node density) may make it more likely to form a long distance link than
other nodes with the same degree. To capture this information, we attach a
latent variable to each node which represents a node's spatial reach. These
variables are inferred from the network structure using a Markov Chain Monte
Carlo algorithm.
We experimentally evaluate our proposed model on 4 different types of
real-world spatial networks (e.g. transportation, biological, infrastructure,
and social). We apply our model to the task of link prediction and achieve up
to a 35% improvement over previous approaches in terms of the area under the
ROC curve. Additionally, we show that our model is particularly helpful for
predicting links between nodes with low degrees. In these cases, we see much
larger improvements over previous models
A Note on Power-Laws of Internet Topology
The three Power-Laws proposed by Faloutsos et al(1999) are important
discoveries among many recent works on finding hidden rules in the seemingly
chaotic Internet topology. In this note, we want to point out that the first
two laws discovered by Faloutsos et al(1999, hereafter, {\it Faloutsos' Power
Laws}) are in fact equivalent. That is, as long as any one of them is true, the
other can be derived from it, and {\it vice versa}. Although these two laws are
equivalent, they provide different ways to measure the exponents of their
corresponding power law relations. We also show that these two measures will
give equivalent results, but with different error bars. We argue that for nodes
of not very large out-degree( in our simulation), the first Faloutsos'
Power Law is superior to the second one in giving a better estimate of the
exponent, while for nodes of very large out-degree() the power law
relation may not be present, at least for the relation between the frequency of
out-degree and node out-degree.Comment: 16 pages, 3 figure
K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases
We consider the -core decomposition of network models and Internet graphs
at the autonomous system (AS) level. The -core analysis allows to
characterize networks beyond the degree distribution and uncover structural
properties and hierarchies due to the specific architecture of the system. We
compare the -core structure obtained for AS graphs with those of several
network models and discuss the differences and similarities with the real
Internet architecture. The presence of biases and the incompleteness of the
real maps are discussed and their effect on the -core analysis is assessed
with numerical experiments simulating biased exploration on a wide range of
network models. We find that the -core analysis provides an interesting
characterization of the fluctuations and incompleteness of maps as well as
information helping to discriminate the original underlying structure
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