Asmall network is more effective than a large network.

That statement is false

The effectiveness of a network is not only correlated with the size of the network. It mostly depend on how you utilize it.

Large networks tend to have advantage in number of opportunities, but it is really hard to manage.

Small network on the other hand, tend to be easier to manage. This mean that you can maintain a strong and personal relationship between members of the network. But it would has less number of opportunities.

Yes, the above statement is true. A small network is more effective than a large network because it is easier to manage. You have to bear in mind that your network is only as strong as the way you manage it.