Diffusion
Diffusion describes how the information spreads in a network. We have broadly touched on this topic already, but it’s interesting to note a couple of things in this section. Miners are clearly incentivized to rapidly spread signals across nodes in the network. However, there are other second-class citizens within the Bitcoin network. Normally, we would care about how diffusion reaches 100% of the nodes in the network. However, in Bitcoin the incentive for non-miners to search for information from miners means that the system only depends on diffusion of information across the mining nodes in the network.
In many presentations, Dr. Craig Wright has been adamant that Bitcoin mirrors biological processes and epidemic models to an astounding degree. Specifically, he references the propagation of transactions and blocks across the network as closely resembling the SEIR-C model of epidemiology (Susceptible, Exposed, Infection, Recovery, Carrier). Shortly after reading Complex Social Networks it became obvious to me why this is true. Vega-Redondo, whose book covers the simpler SIR model, details how social networks display epidemic diffusion varying with different network topologies. In a network, for a signal to spread from one node to another, the nodes must be connected. If there is an intermediary node in between, then the propagation is less likely or slower. In biology, this is analogous to an infection spreading from one person to another. Vega-Redondo specifically cites the number of edges in a network as the key to SIR diffusion in a network. If everyone shakes hands with everyone else, then the disease can spread quickly.
In a network, how does information spread?
In Bitcoin, the answer to this question comes down to our two favorite words: economic incentives. A network that truly mirrors epidemiology would have to spread information as rapidly as a virus through a population. As a miner, I want to announce to the network about the block I just found as rapidly as possible so that it is not orphaned. As a merchant, I want to announce to the network the transaction I just received as rapidly as possible so that even if the customer tries to send a double-spend transaction to a different node, the purchase transaction is the first-seen transaction by miners. Bitcoin’s small-world nature makes this process very easy for everyone involved. Transactions are propagated to over 90% of the network in two seconds or less, and blocks are propagated just as quickly. A network can only have a high level of diffusion if its robustness is similarly high. If some nodes get taken offline, do transactions and blocks still spread quickly? Bitcoin mining displays a remarkable degree of diffusion. Here’s how it resembles biological systems:

Susceptible: All miners are susceptible to any new transaction or block that is propagated across the network. Miners are incentivized to be highly susceptible, eagerly awaiting any new transactions or blocks, because they will lose money if they waste time hashing blocks that have no chance to be included in the chain. .
Exposed: A miner receives a block and determines whether or not they will mine on top of it. Similarly, they receive a transaction and decide whether or not it is valid and it should be added to their mempool.
Infected: A miner decides the block is valid and immediately begins mining on top of this new block. The infection spreads across the entire network as all miners do the same. Similarly, the miner decides a transaction is valid and includes it in their mempool.
Recovery: The miner returns to a state of susceptibility, eagerly awaiting the next block and more transactions.
Carrier: Carrier refers to the non-mining nodes in the network. These agents act as carriers of the “viruses” and simply watch all of this occur. Non-mining nodes “carry” the virus (block/transaction), yet do little to spread it. They don’t generate blocks. Non-mining nodes exist on the outskirts of the network, not in the center of the action where the highly connected nodes constantly spread new viruses.
Taking all of the analysis into account, it becomes increasingly clear that we may truly have something remarkable in front of us: the world’s first biologically inspired network.