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

You Shall not Pass: Avoiding Spurious Paths in Shortest-Path Based Centralities in Multidimensional Complex Networks