Trying to find a list of metrics to measure network effects is rarely difficult, but figuring out which ones to prioritize is. The best way to do this is to put metrics in context.
The most important metrics can vary based on the type of network and its current stage of liquidity. Pre-liquidity, the only thing that matters is figuring out if your network or marketplace has enough activated users to be valuable. Once liquidity is achieved, you need to gauge the health of your growth and unit economics.
The flowcharts in this post lay out a structured approach to measure these dynamics - https://medium.com/breadcrumb/measuring-network-effects-metrics-in-context-e4c3c98dbf4d