The Use Of Networks And Nodes In Cryptocurrencies.
The peer-to-peer network structure in cryptocurrencies is structured according to the consensus mechanism that they are utilizing. For cryptos like Bitcoin and Ethereum which uses a normal proof-of-work consensus mechanism (Ethereum however will eventually move on to Proof of Stake), all the nodes have the same privilege. The idea is to create an egalitarian network. The nodes are not given any special privileges, however, their functions and degree of participation may differ. There is no centralized server/entity, nor is there any hierarchy.
These decentralized cryptocurrencies are structured like that is because of a simple reason, to stay true to their philosophy. The idea is to have a currency system, where everyone is treated as an equal and there is no governing body, which can determine the value of the currency based on a whim. This is true for both bitcoin and Ethereum.
Now, if there is no central system, how would everyone in the system get to know that a certain transaction has happened? The network follows the gossip protocol. Think of how gossip spreads. Suppose Alice sent 3 ETH to Bob. The nodes nearest to her will get to know of this, and then they will tell the nodes closest to them, and then they will tell their neighbors, and this will keep on spreading out until everyone knows.