2,627 research outputs found
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Efficient Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs
Graphs are an important tool to model data in different domains, including
social networks, bioinformatics and the world wide web. Most of the networks
formed in these domains are directed graphs, where all the edges have a
direction and they are not symmetric. Betweenness centrality is an important
index widely used to analyze networks. In this paper, first given a directed
network and a vertex , we propose a new exact algorithm to
compute betweenness score of . Our algorithm pre-computes a set
, which is used to prune a huge amount of computations that do
not contribute in the betweenness score of . Time complexity of our exact
algorithm depends on and it is respectively
and
for unweighted graphs and weighted graphs with positive weights.
is bounded from above by and in most cases, it
is a small constant. Then, for the cases where is large, we
present a simple randomized algorithm that samples from and
performs computations for only the sampled elements. We show that this
algorithm provides an -approximation of the betweenness
score of . Finally, we perform extensive experiments over several real-world
datasets from different domains for several randomly chosen vertices as well as
for the vertices with the highest betweenness scores. Our experiments reveal
that in most cases, our algorithm significantly outperforms the most efficient
existing randomized algorithms, in terms of both running time and accuracy. Our
experiments also show that our proposed algorithm computes betweenness scores
of all vertices in the sets of sizes 5, 10 and 15, much faster and more
accurate than the most efficient existing algorithms.Comment: arXiv admin note: text overlap with arXiv:1704.0735
Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model
Vertex centrality measures are a multi-purpose analysis tool, commonly used
in many application environments to retrieve information and unveil knowledge
from the graphs and network structural properties. However, the algorithms of
such metrics are expensive in terms of computational resources when running
real-time applications or massive real world networks. Thus, approximation
techniques have been developed and used to compute the measures in such
scenarios. In this paper, we demonstrate and analyze the use of neural network
learning algorithms to tackle such task and compare their performance in terms
of solution quality and computation time with other techniques from the
literature. Our work offers several contributions. We highlight both the pros
and cons of approximating centralities though neural learning. By empirical
means and statistics, we then show that the regression model generated with a
feedforward neural networks trained by the Levenberg-Marquardt algorithm is not
only the best option considering computational resources, but also achieves the
best solution quality for relevant applications and large-scale networks.
Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models,
Machine Learning, Regression ModelComment: 8 pages, 5 tables, 2 figures, version accepted at IJCNN 2018. arXiv
admin note: text overlap with arXiv:1810.1176
KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation
We present KADABRA, a new algorithm to approximate betweenness centrality in
directed and undirected graphs, which significantly outperforms all previous
approaches on real-world complex networks. The efficiency of the new algorithm
relies on two new theoretical contributions, of independent interest. The first
contribution focuses on sampling shortest paths, a subroutine used by most
algorithms that approximate betweenness centrality. We show that, on realistic
random graph models, we can perform this task in time
with high probability, obtaining a significant speedup with respect to the
worst-case performance. We experimentally show that this new
technique achieves similar speedups on real-world complex networks, as well.
The second contribution is a new rigorous application of the adaptive sampling
technique. This approach decreases the total number of shortest paths that need
to be sampled to compute all betweenness centralities with a given absolute
error, and it also handles more general problems, such as computing the
most central nodes. Furthermore, our analysis is general, and it might be
extended to other settings.Comment: Some typos correcte
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