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Computing top-k Closeness Centrality Faster in Unweighted Graphs [article]

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2017 arXiv   pre-print
For example, we are able to compute the top k nodes in few dozens of seconds in real-world networks with millions of nodes and edges.  ...  Given a connected graph G=(V,E), the closeness centrality of a vertex v is defined as n-1/∑_w ∈ V d(v,w).  ...  Computing top-k Closeness Centrality Faster in Unweighted Graphs ELISABETTA BERGAMINI, Karlsruhe Institute of Technology  ... 
arXiv:1704.01077v2 fatcat:gc32wvmmdzhczka6rv7h3c7ajy

Computing top-k Closeness Centrality Faster in Unweighted Graphs

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2019 ACM Transactions on Knowledge Discovery from Data  
The second one, Ocl, provides top k closeness centralities with high probability [23] .  ...  Conclusions In this paper we have presented a hardness result on the computation of the most central vertex in a graph, according to closeness centrality.  ... 
doi:10.1145/3344719 fatcat:hfuu46acanb2bl7gqtxoklkuhi

Computing Top-k Closeness Centrality Faster in Unweighted Graphs

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2015 2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Thus, we present a new algorithm for computing this top-k ranking in unweighted graphs. Following the rationale of previous work, our algorithm significantly reduces the number of traversed edges.  ...  The currently best algorithms in practical applications for computing the closeness for all nodes exactly in unweighted graphs are based on breadth-first search (BFS) from every node.  ...  We would like to thank Moritz von Looz for providing the hyperbolic random graphs used in our experiments and numerous contributors to the NetworKit project.  ... 
doi:10.1137/1.9781611974317.6 dblp:conf/alenex/BergaminiBCMM16 fatcat:jys7xwyckfas3m7nrflm6toe6i

Scaling up Group Closeness Maximization [chapter]

Elisabetta Bergamini, Tanya Gonser, Henning Meyerhenke
2018 2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Finally, we study for the first time the correlation between the top-k nodes with highest individual closeness and an approximation of the most central group in large complex networks.  ...  While the identification of the k nodes with highest closeness received significant attention, many applications are actually interested in finding a group of nodes that is central as a whole.  ...  The first element of |S| is computed using the parallel top-k closeness implementation described in [4] .  ... 
doi:10.1137/1.9781611975055.18 dblp:conf/alenex/BergaminiGM18 fatcat:7njuuneb25dnnkqmbx2ilisxcm

New Approximation Algorithms for Forest Closeness Centrality – for Individual Vertices and Vertex Groups [article]

Alexander van der Grinten, Eugenio Angriman, Maria Predari, Henning Meyerhenke
2021 arXiv   pre-print
Moreover, our experiments show that on disconnected graphs, group forest closeness outperforms existing centrality measures in the context of semi-supervised vertex classification.  ...  A measure that is gaining attention is forest closeness centrality; it is closely related to electrical measures using current flow but can also handle disconnected graphs.  ...  accuracy than strategies based on existing centrality measures (including top-k forest closeness).  ... 
arXiv:2101.06192v1 fatcat:v7ks2xvembdcxhr735xehmpbde

K-path centrality

Tharaka Alahakoon, Rahul Tripathi, Nicolas Kourtellis, Ramanuja Simha, Adriana Iamnitchi
2011 Proceedings of the 4th Workshop on Social Network Systems - SNS '11  
Computing K-Path Centrality 2α ln n iterations:Real graphs from online sources and our previous research.Synthetic social graphs of 1K, 10K, 50K, and 100K nodes.Input : Graph G = (V , E ), Array  ...  1 − 1/n 2 -O(κ 3 n 2−2α log n) time on weighted/unweighted graphs, where α ∈ [−1/2, 1/2] controls the tradeoff between accuracy and computation time 3 An empirical demonstration on real and synthetic  ...  Summary We introduced an alternative centrality metric for betweeness centrality, κ-path centrality, that: identifies with high accuracy the top betweenness centrality nodes in a graph; -correlation between  ... 
doi:10.1145/1989656.1989657 dblp:conf/sns/AlahakoonTKSI11 fatcat:bdvwm4ayujfznlcnep7kc3ugsa

Scaling up Group Closeness Maximization [article]

Elisabetta Bergamini, Tanya Gonser, Henning Meyerhenke
2019 arXiv   pre-print
While the identification of the k nodes with highest closeness received significant attention, many applications are actually interested in finding a group of nodes that is central as a whole.  ...  Closeness is a widely-used centrality measure in social network analysis. For a node it indicates the reciprocal of the average shortest-path distance to the other nodes of the network.  ...  closeness and for other helpful discussions on the topic.  ... 
arXiv:1710.01144v2 fatcat:hcwr6pedo5gaziadfyfgqt3ssu

Computing Top-k Closeness Centrality in Fully-dynamic Graphs [chapter]

Patrick Bisenius, Elisabetta Bergamin, Eugenio Angriman, Henning Meyerhenke
2018 2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks.  ...  However, for many applications, it is only necessary to find the k most central nodes and not all closeness values.  ...  Computing the closeness centrality of a node in an unweighted graph requires a complete breadthfirst search (BFS) -or a complete run of Dijkstra's algorithm for weighted graphs.  ... 
doi:10.1137/1.9781611975055.3 dblp:conf/alenex/BiseniusBAM18 fatcat:hf6wjs7uhzdebg6nrv7zdellvy

Estimating graph distance and centrality on shared nothing architectures

Atilla Soner Balkir, Huseyin Oktay, Ian Foster
2014 Concurrency and Computation  
In one experiment, we mined a real-world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20-node  ...  We present a parallel toolkit for pairwise distance computation in massive networks.  ...  For unweighted graphs, Brandes' algorithm [18] can compute betweenness centrality in O.nm/ time.  ... 
doi:10.1002/cpe.3354 fatcat:boqyj6pnibeb5frkqgc5sizqay

Laplacian centrality: A new centrality measure for weighted networks

Xingqin Qi, Eddie Fuller, Qin Wu, Yezhou Wu, Cun-Quan Zhang
2012 Information Sciences  
We also prove an algebraic graph theory result that provides a structural description of the Laplacian centrality measure which is in terms of the number of all kinds of 2-walks.  ...  For unweighted networks where edges are just present or absent and have no weight attached, many centrality measures have been presented, such as degree, betweenness, closeness, eigenvector and subgraph  ...  The subgraph centrality of the vertex i is defined as P 1 k¼0 u k ði;iÞ k! , where u k (i, i) is the number of closed k-walks that vertex i participates in the network.  ... 
doi:10.1016/j.ins.2011.12.027 fatcat:uwd35zzpvrfltlsfk6dg7u55y4

Identifying high betweenness centrality nodes in large social networks

Nicolas Kourtellis, Tharaka Alahakoon, Ramanuja Simha, Adriana Iamnitchi, Rahul Tripathi
2012 Social Network Analysis and Mining  
The randomized algorithm runs in time O(κ^3n^2-2α n) and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of ± n^1/2+ α with probability 1-1/n^2.  ...  It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality.  ...  The authors would also like to acknowledge the use of the computing services provided by Research Computing, University of South Florida.  ... 
doi:10.1007/s13278-012-0076-6 fatcat:kdnyzni375bf5o7hijfyoggdia

Efficient top-k closeness centrality search

Paul W. Olsen, Alan G. Labouseur, Jeong-Hyon Hwang
2014 2014 IEEE 30th International Conference on Data Engineering  
This paper presents a new technique that efficiently finds the k most central entities in terms of closeness centrality.  ...  Since the cost of each centrality computation may vary substantially depending on the choice of the previous computation, our technique schedules centrality computations in a manner that minimizes the  ...  Such a top-k centrality problem can be formally defined as follows: Definition 2: (Top-k Closeness Centrality Problem) Given graph G(V, E), a top-k centrality problem is to find: arg max V ′ ⊆V, V ′ ≥k  ... 
doi:10.1109/icde.2014.6816651 dblp:conf/icde/OlsenLH14 fatcat:bwxgcq6rxza5tjf35o7z4m26pa

Centrality Measures in Complex Networks: A Survey [article]

Akrati Saxena, Sudarshan Iyengar
2020 arXiv   pre-print
values in dynamic networks, methods to identify top-k nodes, approximation algorithms, open research problems related to the domain, and so on.  ...  Some of these centrality measures can be computed using local information of the node, such as degree centrality and semi-local centrality measure.  ...  They further proposed a faster algorithm that involves parallel execution to compute the k-shell in larger graphs.  ... 
arXiv:2011.07190v1 fatcat:obm6lgm6ojaw5iuk3pigvomoo4

Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization

Fredrik D. Johansson, Ankani Chattoraj, Chiranjib Bhattacharyya, Devdatt P. Dubhashi
2015 Neural Information Processing Systems  
We show how the theta function can be interpreted as a measure of diversity in graphs and use this idea, and the graph embedding in algorithms for Max-Cut, correlation clustering and document summarization  ...  We show how it can be computed exactly by semidefinite programming, and how to approximate it using SVM computations.  ...  Acknowledgments This work is supported in part by the Swedish Foundation for Strategic Research (SSF).  ... 
dblp:conf/nips/JohanssonCBD15 fatcat:hlomosgpxbdntdg525rhtlqcly

Betweenness Centrality : Algorithms and Lower Bounds [article]

Shiva Kintali
2008 arXiv   pre-print
In this paper, we present a randomized parallel algorithm and an algebraic method for computing betweenness centrality of all nodes in a network.  ...  Betweenness centrality is the most widely used metric to measure the importance of a node in a network.  ...  Acknowledgements This project is funded by ARC (Algorithms and Randomness Center) of the College of Computing at Georgia Institute of Technology.  ... 
arXiv:0809.1906v2 fatcat:fzkygcvo4jdz7f4dsl3eyaua6i
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