3,518 research outputs found
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
Benchmarking Measures of Network Influence
Identifying key agents for the transmission of diseases (ideas, technology,
etc.) across social networks has predominantly relied on measures of centrality
on a static base network or a temporally flattened graph of agent interactions.
Various measures have been proposed as the best trackers of influence, such as
degree centrality, betweenness, and -shell, depending on the structure of
the connectivity. We consider SIR and SIS propagation dynamics on a
temporally-extruded network of observed interactions and measure the
conditional marginal spread as the change in the magnitude of the infection
given the removal of each agent at each time: its temporal knockout (TKO)
score. We argue that the exhaustive approach of the TKO score makes it an
effective benchmark measure for evaluating the accuracy of other, often more
practical, measures of influence. We find that none of the common network
measures applied to the induced flat graphs are accurate predictors of network
propagation influence on the systems studied; however, temporal networks and
the TKO measure provide the requisite targets for the hunt for effective
predictive measures
Network centrality: an introduction
Centrality is a key property of complex networks that influences the behavior
of dynamical processes, like synchronization and epidemic spreading, and can
bring important information about the organization of complex systems, like our
brain and society. There are many metrics to quantify the node centrality in
networks. Here, we review the main centrality measures and discuss their main
features and limitations. The influence of network centrality on epidemic
spreading and synchronization is also pointed out in this chapter. Moreover, we
present the application of centrality measures to understand the function of
complex systems, including biological and cortical networks. Finally, we
discuss some perspectives and challenges to generalize centrality measures for
multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A
Mathematical modeling approach" by Springe
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