143 research outputs found
The spatial structure of networks
We study networks that connect points in geographic space, such as
transportation networks and the Internet. We find that there are strong
signatures in these networks of topography and use patterns, giving the
networks shapes that are quite distinct from one another and from
non-geographic networks. We offer an explanation of these differences in terms
of the costs and benefits of transportation and communication, and give a
simple model based on the Monte Carlo optimization of these costs and benefits
that reproduces well the qualitative features of the networks studied.Comment: 5 pages, 3 figure
Optimal design of spatial distribution networks
We consider the problem of constructing public facilities, such as hospitals,
airports, or malls, in a country with a non-uniform population density, such
that the average distance from a person's home to the nearest facility is
minimized. Approximate analytic arguments suggest that the optimal distribution
of facilities should have a density that increases with population density, but
does so slower than linearly, as the two-thirds power. This result is confirmed
numerically for the particular case of the United States with recent population
data using two independent methods, one a straightforward regression analysis,
the other based on density dependent map projections. We also consider
strategies for linking the facilities to form a spatial network, such as a
network of flights between airports, so that the combined cost of maintenance
of and travel on the network is minimized. We show specific examples of such
optimal networks for the case of the United States.Comment: 6 pages, 5 figure
Diffusion-based method for producing density equalizing maps
Map makers have long searched for a way to construct cartograms -- maps in
which the sizes of geographic regions such as countries or provinces appear in
proportion to their population or some other analogous property. Such maps are
invaluable for the representation of census results, election returns, disease
incidence, and many other kinds of human data. Unfortunately, in order to scale
regions and still have them fit together, one is normally forced to distort the
regions' shapes, potentially resulting in maps that are difficult to read. Many
methods for making cartograms have been proposed, some of them extremely
complex, but all suffer either from this lack of readability or from other
pathologies, like overlapping regions or strong dependence on the choice of
coordinate axes. Here we present a new technique based on ideas borrowed from
elementary physics that suffers none of these drawbacks. Our method is
conceptually simple and produces useful, elegant, and easily readable maps. We
illustrate the method with applications to the results of the 2000 US
presidential election, lung cancer cases in the State of New York, and the
geographical distribution of stories appearing in the news.Comment: 12 pages, 3 figure
Interplay between function and structure in complex networks
We show that abrupt structural transitions can arise in functionally optimal
networks, driven by small changes in the level of transport congestion. Our
results offer an explanation as to why so many diverse species of network
structure arise in Nature (e.g. fungal systems) under essentially the same
environmental conditions. Our findings are based on an exactly solvable model
system which mimics a variety of biological and social networks. We then extend
our analysis by introducing a novel renormalization scheme involving cost
motifs, to describe analytically the average shortest path across
multiple-ring-and-hub networks. As a consequence, we uncover a 'skin effect'
whereby the structure of the inner multi-ring core can cease to play any role
in terms of determining the average shortest path across the network.Comment: Expanded version of physics/0508228 with additional new result
Optimal Traffic Networks
Inspired by studies on the airports' network and the physical Internet, we
propose a general model of weighted networks via an optimization principle. The
topology of the optimal network turns out to be a spanning tree that minimizes
a combination of topological and metric quantities. It is characterized by a
strongly heterogeneous traffic, non-trivial correlations between distance and
traffic and a broadly distributed centrality. A clear spatial hierarchical
organization, with local hubs distributing traffic in smaller regions, emerges
as a result of the optimization. Varying the parameters of the cost function,
different classes of trees are recovered, including in particular the minimum
spanning tree and the shortest path tree. These results suggest that a
variational approach represents an alternative and possibly very meaningful
path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio
The complex network of global cargo ship movements
Transportation networks play a crucial role in human mobility, the exchange
of goods, and the spread of invasive species. With 90% of world trade carried
by sea, the global network of merchant ships provides one of the most important
modes of transportation. Here we use information about the itineraries of
16,363 cargo ships during the year 2007 to construct a network of links between
ports. We show that the network has several features which set it apart from
other transportation networks. In particular, most ships can be classified in
three categories: bulk dry carriers, container ships and oil tankers. These
three categories do not only differ in the ships' physical characteristics, but
also in their mobility patterns and networks. Container ships follow regularly
repeating paths whereas bulk dry carriers and oil tankers move less predictably
between ports. The network of all ship movements possesses a heavy-tailed
distribution for the connectivity of ports and for the loads transported on the
links with systematic differences between ship types. The data analyzed in this
paper improve current assumptions based on gravity models of ship movements, an
important step towards understanding patterns of global trade and bioinvasion.Comment: 7 figures Accepted for publication by Journal of the Royal Society
Interface (2010) For supplementary information, see
http://www.icbm.de/~blasius/publications.htm
Shape and efficiency in spatial distribution networks
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of the directness of routes from point to point. Using data for several real-world examples, we find that distribution networks appear remarkably close to optimal where both these properties are concerned. We propose two models of network growth that offer explanations of how this situation might arise.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48938/2/jstat6_01_p01015.pd
Understanding disease control: influence of epidemiological and economic factors
We present a local spread model of disease transmission on a regular network
and compare different control options ranging from treating the whole
population to local control in a well-defined neighborhood of an infectious
individual. Comparison is based on a total cost of epidemic, including cost of
palliative treatment of ill individuals and preventive cost aimed at
vaccination or culling of susceptible individuals. Disease is characterized by
pre- symptomatic phase which makes detection and control difficult. Three
general strategies emerge, global preventive treatment, local treatment within
a neighborhood of certain size and only palliative treatment with no
prevention. The choice between the strategies depends on relative costs of
palliative and preventive treatment. The details of the local strategy and in
particular the size of the optimal treatment neighborhood weakly depends on
disease infectivity but strongly depends on other epidemiological factors. The
required extend of prevention is proportional to the size of the infection
neighborhood, but this relationship depends on time till detection and time
till treatment in a non-nonlinear (power) law. In addition, we show that the
optimal size of control neighborhood is highly sensitive to the relative cost,
particularly for inefficient detection and control application. These results
have important consequences for design of prevention strategies aiming at
emerging diseases for which parameters are not known in advance
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
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
Consider designing a transportation network on vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length and capacity scales as for fixed
. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as , where on and on . This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only times
average straight line length. The transition at corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed and the
cost becomes .Comment: 13 page
- …