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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 ?

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A node is a computer that has a copy of the blockchain (or at least a part of it), and broadcasts and receives transactions and blocks from other nodes according to the bitcoin protocol.

The blockchain is more than 100GB, so most people use a lightweight client that connects to a service that connects to a node on the network. Clients are not considered nodes on the network.

A couple of specific examples of each type:

The computers in a mining pool do not need to connect to the network so do not count as nodes (they are only solving a cryptographic problem and don't care about the transaction data). The mining pool will have at least one node that connects to the network to download and broadcast the transaction data, so the number of nodes in a pool depends on how many the maintainers of a specific pool decide to activate.

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From bitcoin.it

Any computer that connects to the Bitcoin network is called a node. Nodes that fully enforce all of the rules of Bitcoin are called full nodes. Most nodes on the network are lightweight nodes instead of full nodes, but full nodes form the backbone of the network.

As long as you connected to bitcoin network so your computer will be considered as bitcoin node.

And for mining pool I'm sorry to have no information :(

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