2,468 research outputs found
The Parameterized Complexity of Centrality Improvement in Networks
The centrality of a vertex v in a network intuitively captures how important
v is for communication in the network. The task of improving the centrality of
a vertex has many applications, as a higher centrality often implies a larger
impact on the network or less transportation or administration cost. In this
work we study the parameterized complexity of the NP-complete problems
Closeness Improvement and Betweenness Improvement in which we ask to improve a
given vertex' closeness or betweenness centrality by a given amount through
adding a given number of edges to the network. Herein, the closeness of a
vertex v sums the multiplicative inverses of distances of other vertices to v
and the betweenness sums for each pair of vertices the fraction of shortest
paths going through v. Unfortunately, for the natural parameter "number of
edges to add" we obtain hardness results, even in rather restricted cases. On
the positive side, we also give an island of tractability for the parameter
measuring the vertex deletion distance to cluster graphs
Scalable Online Betweenness Centrality in Evolving Graphs
Betweenness centrality is a classic measure that quantifies the importance of
a graph element (vertex or edge) according to the fraction of shortest paths
passing through it. This measure is notoriously expensive to compute, and the
best known algorithm runs in O(nm) time. The problems of efficiency and
scalability are exacerbated in a dynamic setting, where the input is an
evolving graph seen edge by edge, and the goal is to keep the betweenness
centrality up to date. In this paper we propose the first truly scalable
algorithm for online computation of betweenness centrality of both vertices and
edges in an evolving graph where new edges are added and existing edges are
removed. Our algorithm is carefully engineered with out-of-core techniques and
tailored for modern parallel stream processing engines that run on clusters of
shared-nothing commodity hardware. Hence, it is amenable to real-world
deployment. We experiment on graphs that are two orders of magnitude larger
than previous studies. Our method is able to keep the betweenness centrality
measures up to date online, i.e., the time to update the measures is smaller
than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on
Knowledge and Data Engineerin
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
A Divide-and-Conquer Algorithm for Betweenness Centrality
The problem of efficiently computing the betweenness centrality of nodes has
been researched extensively. To date, the best known exact and centralized
algorithm for this task is an algorithm proposed in 2001 by Brandes. The
contribution of our paper is Brandes++, an algorithm for exact efficient
computation of betweenness centrality. The crux of our algorithm is that we
create a sketch of the graph, that we call the skeleton, by replacing subgraphs
with simpler graph structures. Depending on the underlying graph structure,
using this skeleton and by keeping appropriate summaries Brandes++ we can
achieve significantly low running times in our computations. Extensive
experimental evaluation on real life datasets demonstrate the efficacy of our
algorithm for different types of graphs. We release our code for benefit of the
research community.Comment: Shorter version of this paper appeared in Siam Data Mining 201
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