8,698 research outputs found
Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
We consider the role of network geometry in two types of diffusion processes:
transport of constant-density information packets with queuing on nodes, and
constant voltage-driven tunneling of electrons. The underlying network is a
homogeneous graph with scale-free distribution of loops, which is constrained
to a planar geometry and fixed node connectivity . We determine properties
of noise, flow and return-times statistics for both processes on this graph and
relate the observed differences to the microscopic process details. Our main
findings are: (i) Through the local interaction between packets queuing at the
same node, long-range correlations build up in traffic streams, which are
practically absent in the case of electron transport; (ii) Noise fluctuations
in the number of packets and in the number of tunnelings recorded at each node
appear to obey the scaling laws in two distinct universality classes; (iii) The
topological inhomogeneity of betweenness plays the key role in the occurrence
of broad distributions of return times and in the dynamic flow. The
maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure
Centrality anomalies in complex networks as a result of model over-simplification
Tremendous advances have been made in our understanding of the properties and
evolution of complex networks. These advances were initially driven by
information-poor empirical networks and theoretical analysis of unweighted and
undirected graphs. Recently, information-rich empirical data complex networks
supported the development of more sophisticated models that include edge
directionality and weight properties, and multiple layers. Many studies still
focus on unweighted undirected description of networks, prompting an essential
question: how to identify when a model is simpler than it must be? Here, we
argue that the presence of centrality anomalies in complex networks is a result
of model over-simplification. Specifically, we investigate the well-known
anomaly in betweenness centrality for transportation networks, according to
which highly connected nodes are not necessarily the most central. Using a
broad class of network models with weights and spatial constraints and four
large data sets of transportation networks, we show that the unweighted
projection of the structure of these networks can exhibit a significant
fraction of anomalous nodes compared to a random null model. However, the
weighted projection of these networks, compared with an appropriated null
model, significantly reduces the fraction of anomalies observed, suggesting
that centrality anomalies are a symptom of model over-simplification. Because
lack of information-rich data is a common challenge when dealing with complex
networks and can cause anomalies that misestimate the role of nodes in the
system, we argue that sufficiently sophisticated models be used when anomalies
are detected.Comment: 14 pages, including 9 figures. APS style. Accepted for publication in
New Journal of Physic
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 transport on wireless networks
We present a study of the application of a variant of a recently introduced
heuristic algorithm for the optimization of transport routes on complex
networks to the problem of finding the optimal routes of communication between
nodes on wireless networks. Our algorithm iteratively balances network traffic
by minimizing the maximum node betweenness on the network. The variant we
consider specifically accounts for the broadcast restrictions imposed by
wireless communication by using a different betweenness measure. We compare the
performance of our algorithm to two other known algorithms and find that our
algorithm achieves the highest transport capacity both for minimum node degree
geometric networks, which are directed geometric networks that model wireless
communication networks, and for configuration model networks that are
uncorrelated scale-free networks.Comment: 5 pages, 4 figure
Vulnerability of weighted networks
In real networks complex topological features are often associated with a
diversity of interactions as measured by the weights of the links. Moreover,
spatial constraints may as well play an important role, resulting in a complex
interplay between topology, weight, and geography. In order to study the
vulnerability of such networks to intentional attacks, these attributes must be
therefore considered along with the topological quantities. In order to tackle
this issue, we consider the case of the world-wide airport network, which is a
weighted heterogeneous network whose evolution and structure are influenced by
traffic and geographical constraints. We first characterize relevant
topological and weighted centrality measures and then use these quantities as
selection criteria for the removal of vertices. We consider different attack
strategies and different measures of the damage achieved in the network. The
analysis of weighted properties shows that centrality driven attacks are
capable to shatter the network's communication or transport properties even at
very low level of damage in the connectivity pattern. The inclusion of weight
and traffic therefore provides evidence for the extreme vulnerability of
complex networks to any targeted strategy and need to be considered as key
features in the finding and development of defensive strategies
Large-scale topological and dynamical properties of Internet
We study the large-scale topological and dynamical properties of real
Internet maps at the autonomous system level, collected in a three years time
interval. We find that the connectivity structure of the Internet presents
average quantities and statistical distributions settled in a well-defined
stationary state. The large-scale properties are characterized by a scale-free
topology consistent with previous observations. Correlation functions and
clustering coefficients exhibit a remarkable structure due to the underlying
hierarchical organization of the Internet. The study of the Internet time
evolution shows a growth dynamics with aging features typical of recently
proposed growing network models. We compare the properties of growing network
models with the present real Internet data analysis.Comment: 13 pages, 15 eps figure
The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
We analyze the global structure of the world-wide air transportation network,
a critical infrastructure with an enormous impact on local, national, and
international economies. We find that the world-wide air transportation network
is a scale-free small-world network. In contrast to the prediction of
scale-free network models, however, we find that the most connected cities are
not necessarily the most central, resulting in anomalous values of the
centrality. We demonstrate that these anomalies arise because of the
multi-community structure of the network. We identify the communities in the
air transportation network and show that the community structure cannot be
explained solely based on geographical constraints, and that geo-political
considerations have to be taken into account. We identify each city's global
role based on its pattern of inter- and intra-community connections, which
enables us to obtain scale-specific representations of the network.Comment: Revised versio
Topology of Cell-Aggregated Planar Graphs
We present new algorithm for growth of non-clustered planar graphs by
aggregation of cells with given distribution of size and constraint of
connectivity k=3 per node. The emergent graph structures are controlled by two
parameters--chemical potential of the cell aggregation and the width of the
cell size distribution. We compute several statistical properties of these
graphs--fractal dimension of the perimeter, distribution of shortest paths
between pairs of nodes and topological betweenness of nodes and links. We show
how these topological properties depend on the control parameters of the
aggregation process and discuss their relevance for the conduction of current
in self-assembled nanopatterns.Comment: 8 pages, 5 figure
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