We will consider the case where we study the number of connected components, 𝑐, while adding edges to a previously empty design. Upon addition of one edge and then a second edge, 𝑐 becomes 𝑛 -1 and then 𝑛 -2. Beyond this point, additional edges may or may not decrease 𝑐. The number of edges required to decrease 𝑐, 𝑘 𝑐 , can be summed as