373,174 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
Measuring the dimension of partially embedded networks
Scaling phenomena have been intensively studied during the past decade in the
context of complex networks. As part of these works, recently novel methods
have appeared to measure the dimension of abstract and spatially embedded
networks. In this paper we propose a new dimension measurement method for
networks, which does not require global knowledge on the embedding of the
nodes, instead it exploits link-wise information (link lengths, link delays or
other physical quantities). Our method can be regarded as a generalization of
the spectral dimension, that grasps the network's large-scale structure through
local observations made by a random walker while traversing the links. We apply
the presented method to synthetic and real-world networks, including road maps,
the Internet infrastructure and the Gowalla geosocial network. We analyze the
theoretically and empirically designated case when the length distribution of
the links has the form P(r) ~ 1/r. We show that while previous dimension
concepts are not applicable in this case, the new dimension measure still
exhibits scaling with two distinct scaling regimes. Our observations suggest
that the link length distribution is not sufficient in itself to entirely
control the dimensionality of complex networks, and we show that the proposed
measure provides information that complements other known measures
Generalized Network Psychometrics: Combining Network and Latent Variable Models
We introduce the network model as a formal psychometric model,
conceptualizing the covariance between psychometric indicators as resulting
from pairwise interactions between observable variables in a network structure.
This contrasts with standard psychometric models, in which the covariance
between test items arises from the influence of one or more common latent
variables. Here, we present two generalizations of the network model that
encompass latent variable structures, establishing network modeling as parts of
the more general framework of Structural Equation Modeling (SEM). In the first
generalization, we model the covariance structure of latent variables as a
network. We term this framework Latent Network Modeling (LNM) and show that,
with LNM, a unique structure of conditional independence relationships between
latent variables can be obtained in an explorative manner. In the second
generalization, the residual variance-covariance structure of indicators is
modeled as a network. We term this generalization Residual Network Modeling
(RNM) and show that, within this framework, identifiable models can be obtained
in which local independence is structurally violated. These generalizations
allow for a general modeling framework that can be used to fit, and compare,
SEM models, network models, and the RNM and LNM generalizations. This
methodology has been implemented in the free-to-use software package lvnet,
which contains confirmatory model testing as well as two exploratory search
algorithms: stepwise search algorithms for low-dimensional datasets and
penalized maximum likelihood estimation for larger datasets. We show in
simulation studies that these search algorithms performs adequately in
identifying the structure of the relevant residual or latent networks. We
further demonstrate the utility of these generalizations in an empirical
example on a personality inventory dataset.Comment: Published in Psychometrik
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