9,064 research outputs found
An Adaptive Version of Brandes\u27 Algorithm for Betweenness Centrality
Betweenness centrality - measuring how many shortest paths pass through a vertex - is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [2001] computes, on an n-vertex and m-edge graph, the betweenness centrality of all vertices in O(nm) worst-case time. In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices. Based on these three algorithmic ingredients, we provide a strengthened worst-case running time analysis for betweenness centrality algorithms. More specifically, we prove an adaptive running time bound O(kn), where k < m is the size of a minimum feedback edge set of the input graph
Two betweenness centrality measures based on Randomized Shortest Paths
This paper introduces two new closely related betweenness centrality measures
based on the Randomized Shortest Paths (RSP) framework, which fill a gap
between traditional network centrality measures based on shortest paths and
more recent methods considering random walks or current flows. The framework
defines Boltzmann probability distributions over paths of the network which
focus on the shortest paths, but also take into account longer paths depending
on an inverse temperature parameter. RSP's have previously proven to be useful
in defining distance measures on networks. In this work we study their utility
in quantifying the importance of the nodes of a network. The proposed RSP
betweenness centralities combine, in an optimal way, the ideas of using the
shortest and purely random paths for analysing the roles of network nodes,
avoiding issues involving these two paradigms. We present the derivations of
these measures and how they can be computed in an efficient way. In addition,
we show with real world examples the potential of the RSP betweenness
centralities in identifying interesting nodes of a network that more
traditional methods might fail to notice.Comment: Minor updates; published in Scientific Report
Controlling nosocomial infection based on structure of hospital social networks
Nosocomial infection raises a serious public health problem, as implied by
the existence of pathogens characteristic to healthcare and hospital-mediated
outbreaks of influenza and SARS. We simulate stochastic SIR dynamics on social
networks, which are based on observations in a hospital in Tokyo, to explore
effective containment strategies against nosocomial infection. The observed
networks have hierarchical and modular structure. We show that healthcare
workers, particularly medical doctors, are main vectors of diseases on these
networks. Intervention methods that restrict interaction between medical
doctors and their visits to different wards shrink the final epidemic size more
than intervention methods that directly protect patients, such as isolating
patients in single rooms. By the same token, vaccinating doctors with priority
rather than patients or nurses is more effective. Finally, vaccinating
individuals with large betweenness centrality is superior to vaccinating ones
with large connectedness to others or randomly chosen individuals, as suggested
by previous model studies. [The abstract of the manuscript has more
information.]Comment: 12 figures, 2 table
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