This page claims there are about 11k nodes in the Bitcoin network. I wonder what exactly constitutes a "node" in the network. For example, if I connect to the network and do nothing, am I still considered in this 11k figure? Or do I have to have an "effect" on the network in some ways, e.g., broadcasting empty blocks or trying to mine honestly. Another question is do mining pools, as a whole, count only as a single node in the network?
In general, what's the precise definition of a node in the context of Bitcoin network ?