First obtain the data from
ColorData["HTML", "ColoRules"]
and eliminate duplicate colors. Then loop through the distance measures built-in for ColorDistance:
https://reference.wolfram.com/language/ref/ColorDistance.html
For each of these, check the four properties listed in the table above (see https://mathworld.wolfram.com/Metric.html and distance[a,b] > 0 for all a != b), collecting pertinent information.
Afterwards, summarize the results in a Table[], using Histogram[] to produce the charts in the last row.