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I set up full-nodes to "help the IOTA network". I asked myself: How does my full-node help the network?

On the full-nodes that are publicly listed in the official wallet app, there are a many light wallets connected. The address of my full-node is not publicly listed and there are no light wallets connected. Probably this counts for my connected neighbors too. So how do full-nodes where no light wallets are connected help those "well known" nodes where are many light wallets connected?

I know that full-nodes receive transactions and send transactions to their neighbors. This way the information of transactions is spread over the full-node network. Question to this point: From all transactions a full-node receives, are there some that the full-node confirms itself and some it does only forward to the neighbors so that one of the neighbors might confirm it? (It's a question, I don't know if it works like this. This is just my attempt to explain why my node may help the network. Busy nodes with lots of connected light wallets and incoming transactions maybe just forward some of the transactions without having the confirmation work).

Where can I find information about how the full-node network looks like? I know it is not a self organizing distributed network, neighbors are manually discovered (e.g #nodesharing) and configured. But is there information how transactions are routed / forwarded. What a full-node does with transactions (confirming them or just forward etc.)?

There is many information about how the transaction data is stored (structure of the tangle etc.) but I'm looking for information about how the full-node network looks like.

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All nodes validate all transactions at this time. In the future this might change when we get swarm nodes, so nodes don't store the whole tangle anymore. Setting up nodes that just broadcast transactions is possible at the moment, you will, however, lose your neighbours very quickly when you redirect several invalid transactions. Some sort of load balancing between nodes, like moving connected wallets to a neighbour with less load should be possible though.

There is no list of all full-nodes. Everyone knows his neighbours but no more. This makes it impossible to take the network down since you can not attack the majority of nodes.

At the moment, you have to choose your node in the wallet, whilst neighbour discovery is already possible using Nelson. Most likely wallets will have an "auto-select" feature similar to Nelson, to find nodes with low load (just speculation though). If you want to help the tangle now, you can share your address with users and list it.

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