  In complex network analysis, centralities based on shortest paths, such as
betweenness and closeness, are widely used. More recently, many complex systems
are being represented by time-varying, multilayer, and time-varying multilayer
networks, i.e. multidimensional (or high order) networks. Nevertheless, it is
well-known that the aggregation process may create spurious paths on the
aggregated view of such multidimensional (high order) networks. Consequently,
these spurious paths may then cause shortest-path based centrality metrics to
produce incorrect results, thus undermining the network centrality analysis. In
this context, we propose a method able to avoid taking into account spurious
paths when computing centralities based on shortest paths in multidimensional
(or high order) networks. Our method is based on MultiAspect Graphs~(MAG) to
represent the multidimensional networks and we show that well-known centrality
algorithms can be straightforwardly adapted to the MAG environment. Moreover,
we show that, by using this MAG representation, pitfalls usually associated
with spurious paths resulting from aggregation in multidimensional networks can
be avoided at the time of the aggregation process. As a result, shortest-path
based centralities are assured to be computed correctly for multidimensional
networks, without taking into account spurious paths that could otherwise lead
to incorrect results. We also present a case study that shows the impact of
spurious paths in the computing of shortest paths and consequently of
shortest-path based centralities, such as betweenness and closeness, thus
illustrating the importance of this contribution.
