I do not manage to use the connectivity filter on the newest versions of Paraview (5.6 and 5.7), using the same procedure that works with version 5.4.1.
Usually, once the dataset is loaded, I use the threshold or the contour filter and then the connectivity filter on the output. This works with version 5.4.1 on my dataset. It would be also possible to use the connectivity filter before threshold or contour.
However, on versions 5.6 and 5.7 the connectivity filter always remains shaded in grey, although it seems to me that the dataset is loaded properly.
Is someone using the connectivity filter with version 5.6 or 5.7?
I am guessing you are using the VisIt bridge to load your nek5000 data. This particular reader plugin creates a Multi-Block dataset and that is why the Connectivity filter is disabled. Your best bet is to use a MergeBlock filter. MergeBlock appends all vtkDataSet leaves of the input composite dataset to a single unstructured grid. Since you seem to only have one block anyway, you will end up with a copy of your unstructuredgrid, and the Connectivity filter will be enabled.
An alternative is to switch to a native Nek5000 reader plugin. I have developed one which is still in pre-production stage. If you build your own ParaView from source, then you can compile the plugin (contact me via direct mail). I could load your nek5000 data as an UnstructuredGrid and Connectivity works just fine.