109,687 research outputs found
Graph measures and network robustness
Network robustness research aims at finding a measure to quantify network
robustness. Once such a measure has been established, we will be able to
compare networks, to improve existing networks and to design new networks that
are able to continue to perform well when it is subject to failures or attacks.
In this paper we survey a large amount of robustness measures on simple,
undirected and unweighted graphs, in order to offer a tool for network
administrators to evaluate and improve the robustness of their network. The
measures discussed in this paper are based on the concepts of connectivity
(including reliability polynomials), distance, betweenness and clustering. Some
other measures are notions from spectral graph theory, more precisely, they are
functions of the Laplacian eigenvalues. In addition to surveying these graph
measures, the paper also contains a discussion of their functionality as a
measure for topological network robustness
On the extremal properties of the average eccentricity
The eccentricity of a vertex is the maximum distance from it to another
vertex and the average eccentricity of a graph is the mean value
of eccentricities of all vertices of . The average eccentricity is deeply
connected with a topological descriptor called the eccentric connectivity
index, defined as a sum of products of vertex degrees and eccentricities. In
this paper we analyze extremal properties of the average eccentricity,
introducing two graph transformations that increase or decrease .
Furthermore, we resolve four conjectures, obtained by the system AutoGraphiX,
about the average eccentricity and other graph parameters (the clique number,
the Randi\' c index and the independence number), refute one AutoGraphiX
conjecture about the average eccentricity and the minimum vertex degree and
correct one AutoGraphiX conjecture about the domination number.Comment: 15 pages, 3 figure
Disentangling different types of El Ni\~no episodes by evolving climate network analysis
Complex network theory provides a powerful toolbox for studying the structure
of statistical interrelationships between multiple time series in various
scientific disciplines. In this work, we apply the recently proposed climate
network approach for characterizing the evolving correlation structure of the
Earth's climate system based on reanalysis data of surface air temperatures. We
provide a detailed study on the temporal variability of several global climate
network characteristics. Based on a simple conceptual view on red climate
networks (i.e., networks with a comparably low number of edges), we give a
thorough interpretation of our evolving climate network characteristics, which
allows a functional discrimination between recently recognized different types
of El Ni\~no episodes. Our analysis provides deep insights into the Earth's
climate system, particularly its global response to strong volcanic eruptions
and large-scale impacts of different phases of the El Ni\~no Southern
Oscillation (ENSO).Comment: 20 pages, 12 figure
Graph Refinement based Airway Extraction using Mean-Field Networks and Graph Neural Networks
Graph refinement, or the task of obtaining subgraphs of interest from
over-complete graphs, can have many varied applications. In this work, we
extract trees or collection of sub-trees from image data by, first deriving a
graph-based representation of the volumetric data and then, posing the tree
extraction as a graph refinement task. We present two methods to perform graph
refinement. First, we use mean-field approximation (MFA) to approximate the
posterior density over the subgraphs from which the optimal subgraph of
interest can be estimated. Mean field networks (MFNs) are used for inference
based on the interpretation that iterations of MFA can be seen as feed-forward
operations in a neural network. This allows us to learn the model parameters
using gradient descent. Second, we present a supervised learning approach using
graph neural networks (GNNs) which can be seen as generalisations of MFNs.
Subgraphs are obtained by training a GNN-based graph refinement model to
directly predict edge probabilities. We discuss connections between the two
classes of methods and compare them for the task of extracting airways from 3D,
low-dose, chest CT data. We show that both the MFN and GNN models show
significant improvement when compared to one baseline method, that is similar
to a top performing method in the EXACT'09 Challenge, and a 3D U-Net based
airway segmentation model, in detecting more branches with fewer false
positives.Comment: Accepted for publication at Medical Image Analysis. 14 page
Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations
Human brain anatomy and function display a combination of modular and
hierarchical organization, suggesting the importance of both cohesive
structures and variable resolutions in the facilitation of healthy cognitive
processes. However, tools to simultaneously probe these features of brain
architecture require further development. We propose and apply a set of methods
to extract cohesive structures in network representations of brain connectivity
using multi-resolution techniques. We employ a combination of soft
thresholding, windowed thresholding, and resolution in community detection,
that enable us to identify and isolate structures associated with different
weights. One such mesoscale structure is bipartivity, which quantifies the
extent to which the brain is divided into two partitions with high connectivity
between partitions and low connectivity within partitions. A second,
complementary mesoscale structure is modularity, which quantifies the extent to
which the brain is divided into multiple communities with strong connectivity
within each community and weak connectivity between communities. Our methods
lead to multi-resolution curves of these network diagnostics over a range of
spatial, geometric, and structural scales. For statistical comparison, we
contrast our results with those obtained for several benchmark null models. Our
work demonstrates that multi-resolution diagnostic curves capture complex
organizational profiles in weighted graphs. We apply these methods to the
identification of resolution-specific characteristics of healthy weighted graph
architecture and altered connectivity profiles in psychiatric disease.Comment: Comments welcom
Cut Tree Construction from Massive Graphs
The construction of cut trees (also known as Gomory-Hu trees) for a given
graph enables the minimum-cut size of the original graph to be obtained for any
pair of vertices. Cut trees are a powerful back-end for graph management and
mining, as they support various procedures related to the minimum cut, maximum
flow, and connectivity. However, the crucial drawback with cut trees is the
computational cost of their construction. In theory, a cut tree is built by
applying a maximum flow algorithm for times, where is the number of
vertices. Therefore, naive implementations of this approach result in cubic
time complexity, which is obviously too slow for today's large-scale graphs. To
address this issue, in the present study, we propose a new cut-tree
construction algorithm tailored to real-world networks. Using a series of
experiments, we demonstrate that the proposed algorithm is several orders of
magnitude faster than previous algorithms and it can construct cut trees for
billion-scale graphs.Comment: Short version will appear at ICDM'1
Network Localization by Shadow Edges
Localization is a fundamental task for sensor networks. Traditional network
construction approaches allow to obtain localized networks requiring the nodes
to be at least tri-connected (in 2D), i.e., the communication graph needs to be
globally rigid. In this paper we exploit, besides the information on the
neighbors sensed by each robot/sensor, also the information about the lack of
communication among nodes. The result is a framework where the nodes are
required to be bi-connected and the communication graph has to be rigid. This
is possible considering a novel typology of link, namely Shadow Edges, that
account for the lack of communication among nodes and allow to reduce the
uncertainty associated to the position of the nodes.Comment: preprint submitted to 2013 European Control Conference, July 17-19
2013, Zurich, Switzerlan
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