Network goods in competitive markets vs. socially optimal network size In networks economics, the socially optimum equilibrium is bigger than the one in perfect competition (see for instance, Easley and Kleinberg 2010, Ch. 17).

Why is that so? Could you provide me with an example?
There are two sorts of network effects a network good might have. It might have consumption externalities (such as with traffic) or it might have positive network externalities (such as with operating systems). The latter case is the case that your link discusses. I don't see a discussion of perfect competition in your link, but if you imagine a model in which consumers choose a level of some good with a positive network externality to buy at some price, equilibrium production should be less than socially optimal for the same reason that there is underproduction in perfect competition with any positive externality -- at the margin, consumers don't take into account the value buying the network good brings to other consumers.