  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 arc 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.
