Jade Robbins Metcalfe’s Law illustrates the relationship between the value from network effects and users in a product, but not how virality can (but not necessarily) occur from it. A product can have Metcalfe’s Law apply (network effects) with no PPV.
AirBnB: The more users that join, the more value the network gains as there are more potential guests and hosts. However, if a user joins they do not need people in their own network to join as well to gain value out of the product and thus it does not have PPV. I may want to tell my friends about AirBnB because it’s an awesome product (Word-of-Mouth), but I do not require them to join to use the product.