84,433 research outputs found
Degree Ranking Using Local Information
Most real world dynamic networks are evolved very fast with time. It is not
feasible to collect the entire network at any given time to study its
characteristics. This creates the need to propose local algorithms to study
various properties of the network. In the present work, we estimate degree rank
of a node without having the entire network. The proposed methods are based on
the power law degree distribution characteristic or sampling techniques. The
proposed methods are simulated on synthetic networks, as well as on real world
social networks. The efficiency of the proposed methods is evaluated using
absolute and weighted error functions. Results show that the degree rank of a
node can be estimated with high accuracy using only samples of the
network size. The accuracy of the estimation decreases from high ranked to low
ranked nodes. We further extend the proposed methods for random networks and
validate their efficiency on synthetic random networks, that are generated
using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be
efficiently used for random networks as well
Estimating and Sampling Graphs with Multidimensional Random Walks
Estimating characteristics of large graphs via sampling is a vital part of
the study of complex networks. Current sampling methods such as (independent)
random vertex and random walks are useful but have drawbacks. Random vertex
sampling may require too many resources (time, bandwidth, or money). Random
walks, which normally require fewer resources per sample, can suffer from large
estimation errors in the presence of disconnected or loosely connected graphs.
In this work we propose a new -dimensional random walk that uses
dependent random walkers. We show that the proposed sampling method, which we
call Frontier sampling, exhibits all of the nice sampling properties of a
regular random walk. At the same time, our simulations over large real world
graphs show that, in the presence of disconnected or loosely connected
components, Frontier sampling exhibits lower estimation errors than regular
random walks. We also show that Frontier sampling is more suitable than random
vertex sampling to sample the tail of the degree distribution of the graph
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
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