12,469 research outputs found
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
Eigenvector-Based Centrality Measures for Temporal Networks
Numerous centrality measures have been developed to quantify the importances
of nodes in time-independent networks, and many of them can be expressed as the
leading eigenvector of some matrix. With the increasing availability of network
data that changes in time, it is important to extend such eigenvector-based
centrality measures to time-dependent networks. In this paper, we introduce a
principled generalization of network centrality measures that is valid for any
eigenvector-based centrality. We consider a temporal network with N nodes as a
sequence of T layers that describe the network during different time windows,
and we couple centrality matrices for the layers into a supra-centrality matrix
of size NTxNT whose dominant eigenvector gives the centrality of each node i at
each time t. We refer to this eigenvector and its components as a joint
centrality, as it reflects the importances of both the node i and the time
layer t. We also introduce the concepts of marginal and conditional
centralities, which facilitate the study of centrality trajectories over time.
We find that the strength of coupling between layers is important for
determining multiscale properties of centrality, such as localization phenomena
and the time scale of centrality changes. In the strong-coupling regime, we
derive expressions for time-averaged centralities, which are given by the
zeroth-order terms of a singular perturbation expansion. We also study
first-order terms to obtain first-order-mover scores, which concisely describe
the magnitude of nodes' centrality changes over time. As examples, we apply our
method to three empirical temporal networks: the United States Ph.D. exchange
in mathematics, costarring relationships among top-billed actors during the
Golden Age of Hollywood, and citations of decisions from the United States
Supreme Court.Comment: 38 pages, 7 figures, and 5 table
Adjustable reach in a network centrality based on current flows
Centrality, which quantifies the "importance" of individual nodes, is among
the most essential concepts in modern network theory. Most prominent centrality
measures can be expressed as an aggregation of influence flows between pairs of
nodes. As there are many ways in which influence can be defined, many different
centrality measures are in use. Parametrized centralities allow further
flexibility and utility by tuning the centrality calculation to the regime most
appropriate for a given network. Here, we identify two categories of centrality
parameters. Reach parameters control the attenuation of influence flows between
distant nodes. Grasp parameters control the centrality's potential to send
influence flows along multiple, often nongeodesic paths. Combining these
categories with Borgatti's centrality types [S. P. Borgatti, Social Networks
27, 55-71 (2005)], we arrive at a novel classification system for parametrized
centralities. Using this classification, we identify the notable absence of any
centrality measures that are radial, reach parametrized, and based on acyclic,
conservative flows of influence. We therefore introduce the ground-current
centrality, which is a measure of precisely this type. Because of its unique
position in the taxonomy, the ground-current centrality has significant
advantages over similar centralities. We demonstrate that, compared to other
conserved-flow centralities, it has a simpler mathematical description.
Compared to other reach centralities, it robustly preserves an intuitive rank
ordering across a wide range of network architectures. We also show that it
produces a consistent distribution of centrality values among the nodes,
neither trivially equally spread (delocalization), nor overly focused on a few
nodes (localization). Other reach centralities exhibit both of these behaviors
on regular networks and hub networks, respectively
Rechecking the Centrality-Lethality Rule in the Scope of Protein Subcellular Localization Interaction Networks
Essential proteins are indispensable for living organisms to maintain life activities and play important roles in the studies of pathology, synthetic biology, and drug design. Therefore, besides experiment methods, many computational methods are proposed to identify essential proteins. Based on the centrality-lethality rule, various centrality methods are employed to predict essential proteins in a Protein-protein Interaction Network (PIN). However, neglecting the temporal and spatial features of protein-protein interactions, the centrality scores calculated by centrality methods are not effective enough for measuring the essentiality of proteins in a PIN. Moreover, many methods, which overfit with the features of essential proteins for one species, may perform poor for other species. In this paper, we demonstrate that the centrality-lethality rule also exists in Protein Subcellular Localization Interaction Networks (PSLINs). To do this, a method based on Localization Specificity for Essential protein Detection (LSED), was proposed, which can be combined with any centrality method for calculating the improved centrality scores by taking into consideration PSLINs in which proteins play their roles. In this study, LSED was combined with eight centrality methods separately to calculate Localization-specific Centrality Scores (LCSs) for proteins based on the PSLINs of four species (Saccharomyces cerevisiae, Homo sapiens, Mus musculus and Drosophila melanogaster). Compared to the proteins with high centrality scores measured from the global PINs, more proteins with high LCSs measured from PSLINs are essential. It indicates that proteins with high LCSs measured from PSLINs are more likely to be essential and the performance of centrality methods can be improved by LSED. Furthermore, LSED provides a wide applicable prediction model to identify essential proteins for different species
Localization of eigenvector centrality in networks with a cut vertex
We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of localization are identified in these structures. One is related to the well-established hub node localization phenomenon and the other two are introduced and characterized here. We gain insights into these problems by deriving the relationship between eigenvector centrality and Katz centrality. This leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix
On the exponential generating function for non-backtracking walks
We derive an explicit formula for the exponential generating function associated with non-backtracking walks around a graph. We study both undirected and directed graphs. Our results allow us to derive computable expressions for non-backtracking versions of network centrality measures based on the matrix exponential. We find that eliminating backtracking walks in this context does not significantly increase the computational expense. We show how the new measures may be interpreted in terms of standard exponential centrality computation on a certain multilayer network. Insights from this block matrix interpretation also allow us to characterize centrality measures arising from general matrix functions. Rigorous analysis on the star graph illustrates the effect of non-backtracking and shows that localization can be eliminated when we restrict to non-backtracking walks. We also investigate the localization issue on synthetic networks
A survey on Human Mobility and its applications
Human Mobility has attracted attentions from different fields of studies such
as epidemic modeling, traffic engineering, traffic prediction and urban
planning. In this survey we review major characteristics of human mobility
studies including from trajectory-based studies to studies using graph and
network theory. In trajectory-based studies statistical measures such as jump
length distribution and radius of gyration are analyzed in order to investigate
how people move in their daily life, and if it is possible to model this
individual movements and make prediction based on them. Using graph in mobility
studies, helps to investigate the dynamic behavior of the system, such as
diffusion and flow in the network and makes it easier to estimate how much one
part of the network influences another by using metrics like centrality
measures. We aim to study population flow in transportation networks using
mobility data to derive models and patterns, and to develop new applications in
predicting phenomena such as congestion. Human Mobility studies with the new
generation of mobility data provided by cellular phone networks, arise new
challenges such as data storing, data representation, data analysis and
computation complexity. A comparative review of different data types used in
current tools and applications of Human Mobility studies leads us to new
approaches for dealing with mentioned challenges
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