Interactively delete data points from a line plot without creating break in line

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Using brush mode, if I delete a data point xi of a line plot with markers, it results in a plot that has no line between points xi-1 and xi+1.
e.g. see the plot here in which I have deleted data point 6
Is there a way to interactively delete a point from a line plot and have the line automatically recreated between adjacent points?

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