Ask HN: Calculating utility of a new member joining a network

Here is what I'm trying to understand.

Let's say I join a network. I gain some utility because of all existing nodes on the network.

At the same time, I add to the utility of a network by becoming a node.

Are there network characteristics which can make this utility asymmetric? e.g. are there circumstances where the marginal increase in the network's utility is greater than the utility gain for the new member?