You first need to identify the core interaction that triggers your network effects. That could be completing a transaction, creating a form of content, etc. Once that's clear, set up a cohort analysis of users who have completed that core interaction. Core interactions within each cohort should increase over time if you have true network effects. Also, newer cohorts should have a higher rate of core interactions (although this can change as you scale because late adopters are likely to be less engaged than early adopters).

With user retention cohorts..and see if your user retention improving for newer cohorts overtime

I heard of something called a North Star metric. The way I viewed this metric is a metric that you can measure within the platform why you are scaling. It can focus you in and hone you in on a strategy to what is working in the model.

With sources of traffic, As the network grows, you can measure how much traffic/transactions on the network are generated internally and if they are arising from the network itself vs. from external sources

Isn't that customer retention?