The rate of change of comments count & upvotes is considered as the metric. More the comments & upvotes fluctuate, more the activity.
The top stories are grabbed from the official HN API.
Cumulative Score = sum(no of comments, no of votes) (for all top stories)
This score is calculated, every 60 seconds. The fluctuation of this values, gives an indication of the activity level on the site.
where t is time,
F(t) = cumulative_score @ time t
fluctuation = |F(t) - F(t-1)|
A log(fluctuation) is taken to generate actual datapoints for the graph. This is to minize the bandwidth of the data series.
Also, Savitzky-Golay filter is applied on the data series to smooth the graph.
This is just a very rough, approximate sketch of the activity on the site. It doesn't aim to be the most accurate indicator and cannot be taken as precise data for serious projects.