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Article

Finding Top-k Nodes for Temporal Closeness in Large Temporal Graphs

1
IRIF, CNRS, Université de Paris, F-75013 Paris, France
2
CNRS, LIP6, Sorbonne Université, F-75005 Paris, France
3
Dipartimento di Statistica, Informatica, Applicazioni “Giuseppe Parenti”, Università degli Studi di Firenze, I-50134 Firenze, Italy
*
Author to whom correspondence should be addressed.
On-leave from Università degli Studi di Firenze, DiMaI, I-50134 Firenze, Italy.
Algorithms 2020, 13(9), 211; https://doi.org/10.3390/a13090211
Received: 15 July 2020 / Revised: 20 August 2020 / Accepted: 26 August 2020 / Published: 29 August 2020
(This article belongs to the Special Issue Big Data Algorithmics)
The harmonic closeness centrality measure associates, to each node of a graph, the average of the inverse of its distances from all the other nodes (by assuming that unreachable nodes are at infinite distance). This notion has been adapted to temporal graphs (that is, graphs in which edges can appear and disappear during time) and in this paper we address the question of finding the top-k nodes for this metric. Computing the temporal closeness for one node can be done in O(m) time, where m is the number of temporal edges. Therefore computing exactly the closeness for all nodes, in order to find the ones with top closeness, would require O(nm) time, where n is the number of nodes. This time complexity is intractable for large temporal graphs. Instead, we show how this measure can be efficiently approximated by using a “backward” temporal breadth-first search algorithm and a classical sampling technique. Our experimental results show that the approximation is excellent for nodes with high closeness, allowing us to detect them in practice in a fraction of the time needed for computing the exact closeness of all nodes. We validate our approach with an extensive set of experiments. View Full-Text
Keywords: temporal graph; link stream; temporal path; temporal closeness; montecarlo method temporal graph; link stream; temporal path; temporal closeness; montecarlo method
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MDPI and ACS Style

Crescenzi, P.; Magnien, C.; Marino, A. Finding Top-k Nodes for Temporal Closeness in Large Temporal Graphs. Algorithms 2020, 13, 211. https://doi.org/10.3390/a13090211

AMA Style

Crescenzi P, Magnien C, Marino A. Finding Top-k Nodes for Temporal Closeness in Large Temporal Graphs. Algorithms. 2020; 13(9):211. https://doi.org/10.3390/a13090211

Chicago/Turabian Style

Crescenzi, Pierluigi, Clémence Magnien, and Andrea Marino. 2020. "Finding Top-k Nodes for Temporal Closeness in Large Temporal Graphs" Algorithms 13, no. 9: 211. https://doi.org/10.3390/a13090211

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