1,477 research outputs found
A measure of centrality based on the spectrum of the Laplacian
We introduce a family of new centralities, the k-spectral centralities.
k-Spectral centrality is a measurement of importance with respect to the
deformation of the graph Laplacian associated with the graph. Due to this
connection, k-spectral centralities have various interpretations in terms of
spectrally determined information.
We explore this centrality in the context of several examples. While for
sparse unweighted networks 1-spectral centrality behaves similarly to other
standard centralities, for dense weighted networks they show different
properties. In summary, the k-spectral centralities provide a novel and useful
measurement of relevance (for single network elements as well as whole
subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table
Resistance distance, information centrality, node vulnerability and vibrations in complex networks
We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality
A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks
We propose a new measure of vulnerability of a node in a complex network. The
measure is based on the analogy in which the nodes of the network are
represented by balls and the links are identified with springs. We define the
measure as the node displacement, or the amplitude of vibration of each node,
under fluctuation due to the thermal bath in which the network is supposed to
be submerged. We prove exact relations among the thus defined node
displacement, the information centrality and the Kirchhoff index. The relation
between the first two suggests that the node displacement has a better
resolution of the vulnerability than the information centrality, because the
latter is the sum of the local node displacement and the node displacement
averaged over the entire network.Comment: 27 page
Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths
We introduce several novel and computationally efficient methods for
detecting "core--periphery structure" in networks. Core--periphery structure is
a type of mesoscale structure that includes densely-connected core vertices and
sparsely-connected peripheral vertices. Core vertices tend to be well-connected
both among themselves and to peripheral vertices, which tend not to be
well-connected to other vertices. Our first method, which is based on
transportation in networks, aggregates information from many geodesic paths in
a network and yields a score for each vertex that reflects the likelihood that
a vertex is a core vertex. Our second method is based on a low-rank
approximation of a network's adjacency matrix, which can often be expressed as
a tensor-product matrix. Our third approach uses the bottom eigenvector of the
random-walk Laplacian to infer a coreness score and a classification into core
and peripheral vertices. We also design an objective function to (1) help
classify vertices into core or peripheral vertices and (2) provide a
goodness-of-fit criterion for classifications into core versus peripheral
vertices. To examine the performance of our methods, we apply our algorithms to
both synthetically-generated networks and a variety of networks constructed
from real-world data sets.Comment: This article is part of EJAM's December 2016 special issue on
"Network Analysis and Modelling" (available at
https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/issue/journal-ejm-volume-27-issue-6/D245C89CABF55DBF573BB412F7651ADB
Graphs and networks theory
This chapter discusses graphs and networks theory
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