The sum of the squared revenue shares of all customers: near 0 for a fragmented base, 1 for a single customer.
HHI squares each customer's share and sums them, so large shares count for much more than small ones and the whole distribution is reflected in one number. It moves when the largest customer grows at the expense of the next nine, a change the top-ten ratio cannot see. Antitrust thresholds for market concentration do not transfer to customer lists. See concentration ratio versus Herfindahl index.
Each customer's share of revenue, squared, and summed across all customers.
Ten customers at 5 percent each plus a long tail gives about 0.03. One at 41 percent and nine at 1 percent gives about 0.17. Both have a top-ten share of 50 percent.
Antitrust thresholds for markets applied to a customer list. They are for a different question.