561 research outputs found
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
Disease spread through animal movements: a static and temporal network analysis of pig trade in Germany
Background: Animal trade plays an important role for the spread of infectious
diseases in livestock populations. As a case study, we consider pig trade in
Germany, where trade actors (agricultural premises) form a complex network. The
central question is how infectious diseases can potentially spread within the
system of trade contacts. We address this question by analyzing the underlying
network of animal movements.
Methodology/Findings: The considered pig trade dataset spans several years
and is analyzed with respect to its potential to spread infectious diseases.
Focusing on measurements of network-topological properties, we avoid the usage
of external parameters, since these properties are independent of specific
pathogens. They are on the contrary of great importance for understanding any
general spreading process on this particular network. We analyze the system
using different network models, which include varying amounts of information:
(i) static network, (ii) network as a time series of uncorrelated snapshots,
(iii) temporal network, where causality is explicitly taken into account.
Findings: Our approach provides a general framework for a
topological-temporal characterization of livestock trade networks. We find that
a static network view captures many relevant aspects of the trade system, and
premises can be classified into two clearly defined risk classes. Moreover, our
results allow for an efficient allocation strategy for intervention measures
using centrality measures. Data on trade volume does barely alter the results
and is therefore of secondary importance. Although a static network description
yields useful results, the temporal resolution of data plays an outstanding
role for an in-depth understanding of spreading processes. This applies in
particular for an accurate calculation of the maximum outbreak size.Comment: main text 33 pages, 17 figures, supporting information 7 pages, 7
figure
Multilayer Networks in a Nutshell
Complex systems are characterized by many interacting units that give rise to
emergent behavior. A particularly advantageous way to study these systems is
through the analysis of the networks that encode the interactions among the
system's constituents. During the last two decades, network science has
provided many insights in natural, social, biological and technological
systems. However, real systems are more often than not interconnected, with
many interdependencies that are not properly captured by single layer networks.
To account for this source of complexity, a more general framework, in which
different networks evolve or interact with each other, is needed. These are
known as multilayer networks. Here we provide an overview of the basic
methodology used to describe multilayer systems as well as of some
representative dynamical processes that take place on top of them. We round off
the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio
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