1,377 research outputs found
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
Channels of Synthesis Forty Years On: Integrated Analysis of Spatial Economic Systems
Isard’s vision of integrated modeling that was laid out in the 1960s book Methods of Regional Science provided a road map for the development of more sophisticated analysis of spatial economic systems. Some forty years later, we look back at this vision and trace developments in a sample of three areas – demographic-econometric integrated modeling, spatial interaction modeling, and environmental-economic modeling. Attention will be focused on methodological advances and their motivation by new developments in theory as well as innovations in the applications of these models to address new policy challenges. Underlying the discussion will be an evaluation of the way in which spatial issues have been addressed, ranging from concerns with regionalization to issues of spillovers and spatial correlation.Spatial economic system, Integrated analysis,
MultiAspect Graphs: Algebraic representation and algorithms
We present the algebraic representation and basic algorithms for MultiAspect
Graphs (MAGs). A MAG is a structure capable of representing multilayer and
time-varying networks, as well as higher-order networks, while also having the
property of being isomorphic to a directed graph. In particular, we show that,
as a consequence of the properties associated with the MAG structure, a MAG can
be represented in matrix form. Moreover, we also show that any possible MAG
function (algorithm) can be obtained from this matrix-based representation.
This is an important theoretical result since it paves the way for adapting
well-known graph algorithms for application in MAGs. We present a set of basic
MAG algorithms, constructed from well-known graph algorithms, such as degree
computing, Breadth First Search (BFS), and Depth First Search (DFS). These
algorithms adapted to the MAG context can be used as primitives for building
other more sophisticated MAG algorithms. Therefore, such examples can be seen
as guidelines on how to properly derive MAG algorithms from basic algorithms on
directed graph. We also make available Python implementations of all the
algorithms presented in this paper.Comment: 59 pages, 6 figure
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201
Human mobility: Models and applications
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordRecent years have witnessed an explosion of extensive geolocated datasets related to human movement, enabling scientists to quantitatively study individual and collective mobility patterns, and to generate models that can capture and reproduce the spatiotemporal structures and regularities in human trajectories. The study of human mobility is especially important for applications such as estimating migratory flows, traffic forecasting, urban planning, and epidemic modeling. In this survey, we review the approaches developed to reproduce various mobility patterns, with the main focus on recent developments. This review can be used both as an introduction to the fundamental modeling principles of human mobility, and as a collection of technical methods applicable to specific mobility-related problems. The review organizes the subject by differentiating between individual and population mobility and also between short-range and long-range mobility. Throughout the text the description of the theory is intertwined with real-world applications.US Army Research Offic
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