The Bitcoin network is a peer to peer network or a decentralized network where is no central point of failure or command. All the nodes, or computers, that participate in the network are equal. The hierarchy is absent and there is no topology because the network is flat.
The CCurrency Bitcoin network is a list of nodes running the Bitcoin peer to peer protocol with other protocols such as a stratum, used for lightweight mobile wallets (where the full blockchain is not downloaded) or for mining.
However the network is flat, and all nodes are equal. And some nodes or computers perform the different task.
A full node does routing, holds a full copy of the blockchain database, performing mining and provides wallet services. Any node must provide the routing function to participate in the network. Routing is just another method to say that the code validates and passes on transactions and block as well as discovering and maintaining connections to other nodes, whether they are full nodes or not.
Some nodes don’t have a full copy of the blockchain and verify transactions by using the Simplified Payment Verification, or SPV.
Mining nodes, that start specialized application specific integrated chips for solving the proof of work algorithm. Some of the mining nodes are full nodes whilst others are lightweight participating in pool mining and using a pool server to maintain a full node.
Wallets can be a full node – as is the case with downloading the full bitcoin client onto your desktop. Mobile wallets, however, can’t hold the entire blockchain through space requirements and are essentially simplified payment verification nodes or lightweight nodes.
Apart from these main classifications, there are also other servers and nodes running other protocols - such as alternative wallets and specialized mining pools.
The main Bitcoin network contains about 7000-10000 nodes at a time.
When you join the network for the first time a new node should discover at least one other existing node – geographical location takes no precedence in this procedure. The new node sends a series of messages and then if the other node wishes to form a connection it replies.
The new node should form new connections to the network. Because sometimes some nodes go offline from time to time as people switch off their computers. Then the new node has meshed into the network and resilience is created.
If you want to run a full node you need to wait a little bit while all the transactions since Bitcoins genesis in 2009 will be downloaded. It's was done by requesting other nodes to send all their information to you, and because not to overload them, this might be done in conjunction with other nodes.
But there is good news.
If you want your own wallet on your phone or need to run the Bitcoin full client, you can just use Coinbase’s or blockchain.io’s simplified version and set it up in a moment. By the way, It's very simple. Good luck.