Another often overlooked viral loop concept is cycle time. That's the average time it takes to complete one loop, e.g. the cycle from sending out an invite to the person who was invited sending out an invite.
In other words, Viral cycle time is the wavelength of viral loops. It's often overlooked (at least initially) because the focus is usually on just getting exponential.
Cycle time is important because along with the k-factor, cycle time determines growth trajectory. You can be exponential, but still grow really really slowly. A decent analogy would be radioactive material with a really long half life. It could take you a while to double...
Like anything, though, there are opportunities to optimize. For example, if your viral loop is based on email (often is), you can send out varying kinds of reminders at opportune times. You can also try to create a sense of urgency.
Another way to optimize is to shorten the times between sign up and invite, e.g. by making it part of the process and/or by making it accessible from every page. And finally, the third part of the cycle is the time from click through to sign-up, which can be reduced by forcing sign-up to get access to content and/or again creating urgency to sign up.
Cycle times are pretty important in other areas too. For example, the lean startup movement talks about reducing the cycle time of getting code out the door and into customers' hands, based on the idea that the faster you iterate, the faster your product will achieve market penetration.