Geodesic
Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality
Journal of Graph Algorithms and Applications, Tome 27 (2023) no. 3, pp. 173-194.

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In static graphs, the betweenness centrality of a graph vertex measures how many times this vertex is part of a shortest path between any two graph vertices. Betweenness centrality is efficiently computable and it is a fundamental tool in network science. Continuing and extending previous work, we study the efficient computability of betweenness centrality in temporal graphs (graphs with fixed vertex set but time-varying edge sets). Unlike in the static case, there are numerous natural notions of being a ''shortest'' temporal path (walk). Depending on which notion is used, it was already observed that the problem is #P-hard in some cases while polynomial-time solvable in others. In this conceptual work, we contribute towards classifying what a ''shortest path (walk) concept'' has to fulfill in order to gain polynomial-time computability of temporal betweenness centrality.
DOI : 10.7155/jgaa.00619
Keywords: temporal graphs, temporal paths and walks, network science, network centrality measures, counting complexity 
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Maciej Rymar; Hendrik Molter; André Nichterlein; Rolf Niedermeier. Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality. Journal of Graph Algorithms and Applications, Tome 27 (2023) no. 3, pp. 173-194. doi : 10.7155/jgaa.00619. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00619/

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