For newcomers, we explain what Peer-to-Peer communication is and how the direct hand-to-hand transfer of a banknote differs from user interaction through the blockchain.
Alice and Bob
If Alice meets Bob and hands him a ten-dollar bill, a Peer-to-Peer (P2P) interaction has occurred. Both participants see each other face to face. It is therefore the simplest form of mutual interaction.
A ten-dollar bill is a physical object and therefore physical contact was necessary for the transfer of value. Alice had to take the bill out of her wallet and hand it to Bob, who put it in his own wallet.
However, money also has a digital form. Alice and Bob can set up bank accounts which are essentially digital wallets. Alice can send Bob $10 from her digital wallet to Bob's digital wallet through a wire transfer. This form of communication works at a distance. Alice and Bob may be thousands of kilometers apart.
Note that a bank (or multiple banks) acts as an intermediary between Alice and Bob. Banks provide a service to their clients and have full power over the money that clients have deposited with them. They can collect transaction data, misuse client data, or even block transactions and freeze an account.
Interaction through banks is considered centralized. An intermediary enters the interaction between Alice and Bob, who has the ability to prevent or complicate the transfer of value.
Blockchain is a decentralized network in which coins and tokens with a certain value can exist. Dollars can be tokenized. This form of money is called stablecoins.
Alice and Bob can use the blockchain and transfer value in a P2P manner. They do not need a third party or an intermediary to interact with each other. Alice and Bob can use blockchain to create and verify transactions that are recorded in a distributed ledger, which is shared and maintained by a network of nodes. Each node in the network can act as both a sender and a receiver of transactions, as well as a validator and propagator of blocks.
Alice uses a blockchain wallet and creates a transaction which she then submits to the blockchain network. The network, i.e. all nodes in the network, verify the transaction and if it is valid, it will be permanently stored in the distributed ledger through a new block. A value has been transferred through the transaction. If Bob looks into his own blockchain wallet, he will find that he has received value (tokens) from Alice.
The blockchain network can be seen as a similar service or tool provided by banks because it enabled the transfer of value between Alice and Bob. Nodes, especially block producer nodes, are not considered intermediaries during P2P communication between Alice and Bob because they do not have full control over the transaction and cannot change, cancel or reverse it in any way. All valid transactions always get into the block. Block producer nodes are simply responsible for validating and propagating transactions and blocks to the network, following the consensus rules that are agreed upon by all nodes.
Block producer nodes are not intermediaries, but rather facilitators of the P2P network. Blockchain networks are decentralized and secure as long as there is enough diversity, participation, and innovation in the ecosystem.
The more independent block producer nodes there are in the network, the more decentralized and secure the network is. As diversity and participation decline, the quality of key network features declines. We will talk about some later.

Blockchain simplifies the mutual interaction between Alice and Bob compared to the traditional financial system. Blockchain enables a mutual digital Peer-to-Peer form of interaction between participants. Note that banks cannot operate in a Peer-to-Peer way because there is always a centralized intermediary between the participants, often there are more of them.
How people connect to the blockchain
Alice and Bob can communicate P2P only if they both run their own full nodes. In the case of Cardano, they would have to run the Daedalus wallet, which is installed on users' computers together with the Cardano node.

However, most users do not run their own full node, as it is user-unfriendly and demanding on computer resources (mainly storage). If users start a wallet (together with the full node) before they want to use it, it must be synchronized with the blockchain. Node downloads and validates all newly added blocks including transactions. This may take some time.
Due to greater comfort, users prefer to use so-called light wallets. These wallets are often just browser extensions that connect to servers operated by third parties. These servers are connected to the blockchain network. Light wallets are not directly connected to the blockchain network, so they do not have their own copy of the ledger with them. That is why they are called light.
If you use Trezor and Ledger hardware wallets in a normal way (without your own full node), you also connect to servers operated by vendors.
Alice and Bob no longer communicate in a direct P2P manner, as they must trust third-party servers. They sacrificed P2P communication for higher user comfort and have to trust a third party regarding the connection to the blockchain network.
Third parties are theoretically a weak point of decentralization because if they shut down the server, users will lose connection to the blockchain network. Their digital assets are safe as long as users hold the private keys used to sign transactions. They can connect to the blockchain network in a different way (through a different wallet) and integrate with other users.

Is it possible to communicate in a P2P way and at the same time not be forced to operate a full node? Is it possible to have a light wallet with full-node security? Yes, Mithril technology will enable the creation of a trustless light wallet with full node security.

Once light Mithril wallets can be implemented, Alice and Bob will not have to rely on third-party servers. They will be capable of P2P communication from user-friendly wallets that can run on a mobile phone. Note that the picture with the Daedalus wallets looks very similar to the one with the Mithril wallets.
P2P communication and decentralization
The degree of decentralization, especially the number of block producer nodes, directly affects the quality of P2P communication between users. Beside other properties, users expect inclusion (no need to ask anyone for permission to use the network), resistance to censorship, and fairness (all users are equal) from a decentralized network.
These features are achieved mainly through the high participation of block producers and their diversity. This makes it impossible for all block producers to know each other. They are from different geographical locations and have different incentives. Usually, the biggest incentive is the reward from the network. If one or several block producers deviate from the expected performance of their function, users expect that it will have only a minimal effect on the overall functioning of the network. If the majority of block producers perform their activities in accordance with the expectations of users, the network will be successful and used.
The biggest threat to blockchain networks is declining decentralization. If the number of block producers is low, or if a few of them are significantly dominant, the quality of features that users expect may decrease.
For example, if a dominant block producer with a 30% share starts censoring the transactions of some users, they will be worse off than others, as their transactions may be processed later. Another smaller block producer can include in the block those transactions that the dominant producer censors, but the fairness will be violated.
Ideally, there should be so many block producers in the network that even if you send one transaction every minute for 1 hour, it will be included in the block by a different block producer (almost) every time. If this is the case, it means that no entity has dominance in the network.
Although there are multi-pool operators in the Cardano network, Cardano meets the requirements for a high degree of decentralization. Cardano produces a new block every 20 seconds, so 180 per hour. There are 1100 active pools that produce blocks. Cardano would have a chance to pass our decentralization test.
Of course, this is just a hastily invented metric for measuring decentralization. I hope you get the point. Decentralization would be even better if you sent a transaction every minute for 24 hours and each time a different producer included it in the block. Cardano would not pass this test, as such a requirement is too ambitious for current blockchain networks. It required a minimum of 1440 independent block producers on the network (and of course a little luck).
See which entities produced the last 20 blocks in a row in the 3 largest decentralized networks in the top 10 (Bitcoin has an average block time of 10 minutes and Ethereum 12 seconds).

Innovations are another necessary part of blockchain projects, as they allow to maintain decentralization at a high level. All networks will naturally tend towards centralization over time. The teams, along with the community, will have a lot of work to do to keep the networks decentralized and economically sustainable in the long term. It is sometimes said that decentralization is like democracy. It is necessary to take care of it, or we can lose it.
Conclusion
The blockchain network can reduce the number of participants between Alice and Bob to a minimum, especially if they use their own full node. In such a case, only the blockchain network (block producers) and no third parties are among the participants. The current infrastructure of most networks is dependent on third-party servers, as people want to use light wallets or centralized services (exchanges). Technology like Mithril can ensure P2P communication and high-quality user comfort at the same time. We will have to wait a while for Mithril to be used in wallets.