4,768 research outputs found
The effects of spatial constraints on the evolution of weighted complex networks
Motivated by the empirical analysis of the air transportation system, we
define a network model that includes geographical attributes along with
topological and weight (traffic) properties. The introduction of geographical
attributes is made by constraining the network in real space. Interestingly,
the inclusion of geometrical features induces non-trivial correlations between
the weights, the connectivity pattern and the actual spatial distances of
vertices. The model also recovers the emergence of anomalous fluctuations in
the betweenness-degree correlation function as first observed by Guimer\`a and
Amaral [Eur. Phys. J. B {\bf 38}, 381 (2004)]. The presented results suggest
that the interplay between weight dynamics and spatial constraints is a key
ingredient in order to understand the formation of real-world weighted
networks
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
LexRank: Graph-based Lexical Centrality as Salience in Text Summarization
We introduce a stochastic graph-based method for computing relative
importance of textual units for Natural Language Processing. We test the
technique on the problem of Text Summarization (TS). Extractive TS relies on
the concept of sentence salience to identify the most important sentences in a
document or set of documents. Salience is typically defined in terms of the
presence of particular important words or in terms of similarity to a centroid
pseudo-sentence. We consider a new approach, LexRank, for computing sentence
importance based on the concept of eigenvector centrality in a graph
representation of sentences. In this model, a connectivity matrix based on
intra-sentence cosine similarity is used as the adjacency matrix of the graph
representation of sentences. Our system, based on LexRank ranked in first place
in more than one task in the recent DUC 2004 evaluation. In this paper we
present a detailed analysis of our approach and apply it to a larger data set
including data from earlier DUC evaluations. We discuss several methods to
compute centrality using the similarity graph. The results show that
degree-based methods (including LexRank) outperform both centroid-based methods
and other systems participating in DUC in most of the cases. Furthermore, the
LexRank with threshold method outperforms the other degree-based techniques
including continuous LexRank. We also show that our approach is quite
insensitive to the noise in the data that may result from an imperfect topical
clustering of documents
Statistical Analysis of Bus Networks in India
Through the past decade the field of network science has established itself
as a common ground for the cross-fertilization of exciting inter-disciplinary
studies which has motivated researchers to model almost every physical system
as an interacting network consisting of nodes and links. Although public
transport networks such as airline and railway networks have been extensively
studied, the status of bus networks still remains in obscurity. In developing
countries like India, where bus networks play an important role in day-to-day
commutation, it is of significant interest to analyze its topological structure
and answer some of the basic questions on its evolution, growth, robustness and
resiliency. In this paper, we model the bus networks of major Indian cities as
graphs in \textit{L}-space, and evaluate their various statistical properties
using concepts from network science. Our analysis reveals a wide spectrum of
network topology with the common underlying feature of small-world property. We
observe that the networks although, robust and resilient to random attacks are
particularly degree-sensitive. Unlike real-world networks, like Internet, WWW
and airline, which are virtual, bus networks are physically constrained. The
presence of various geographical and economic constraints allow these networks
to evolve over time. Our findings therefore, throw light on the evolution of
such geographically and socio-economically constrained networks which will help
us in designing more efficient networks in the future.Comment: Submitted to PLOS ON
Topics in social network analysis and network science
This chapter introduces statistical methods used in the analysis of social
networks and in the rapidly evolving parallel-field of network science.
Although several instances of social network analysis in health services
research have appeared recently, the majority involve only the most basic
methods and thus scratch the surface of what might be accomplished.
Cutting-edge methods using relevant examples and illustrations in health
services research are provided
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