In the vast and enigmatic digital universe of blockchain, a pivotal player emerges – the Full Node. Envision joining a game governed by specific rules; Full Nodes are akin to "game referees" meticulously adhering to these rules while vigilantly overseeing others' compliance.

A Full Node is more than just a computer; it's equipped with comprehensive blockchain software, functioning as a super ledger chronicling all transactions, capable of autonomously verifying the legitimacy of each transaction and block, thereby ensuring the authenticity of information on the blockchain. In essence, Full Nodes embody the trust foundation of blockchain, safeguarding the system's fairness and security through computational power.

Why Are Full Nodes So Vital?

Firstly, they guarantee data integrity. The crux of blockchain lies in its immutability, which Full Nodes reinforce by meticulously validating every transaction within new blocks against protocol guidelines, preventing fraud such as double-spending. They act as meticulous auditors, ensuring each transaction's veracity down to the last cent.

Secondly, they shield the network from attacks. The multitude of Full Nodes significantly raises the bar for hackers attempting to tamper with records. To alter history, theoretically, over 50% of the network's Full Nodes must be controlled, an almost insurmountable task in extensive, decentralized networks. Hence, a higher number of operational Full Nodes translates to a more secure network, akin to a fortress guarded by thousands of loyal sentinels deterring adversaries.

How Do Full Nodes Operate?

Upon a transaction occurrence, it's broadcast across the network. Full Nodes receive these requests, scrutinizing them according to blockchain protocols: verifying sender’s sufficient funds, correct transaction formatting, among others. Once cleared, transactions await in a pool to be included in upcoming blocks.

Then, miners (or validators in certain networks) compete to solve a complex mathematical puzzle. The victor adds a batch of transactions into a new block, broadcasting it to all Full Nodes. Each node independently verifies the block's transactions and its link to the previous block, accepting and appending it to their blockchain copy only if everything checks out, thus extending the blockchain.

The Cost and Reward of Running a Full Node

Operating a Full Node necessitates hardware resources, including ample storage for the complete blockchain data and a stable internet connection for real-time transaction updates. For large blockchains like Bitcoin, this means storing hundreds of GBs or more, a substantial burden for average users. However, in return, Full Node operators enjoy top-tier security and privacy, directly accessing blockchain data without third-party reliance, invaluable for data sovereignty advocates.

While running a Full Node typically doesn't yield direct economic rewards (except when mining), it significantly contributes to the blockchain community, fostering the ecosystem's health and stability. Some projects incentivize Full Node operation through token airdrops or other benefits, enhancing decentralization. 

In summary, Full Nodes are blockchain's unsung guardians, ensuring every transaction's veracity and the system's transparency. Their presence enables blockchain to be the potent, reliable, and trustworthy technology it is today. For anyone concerned with data security and financial freedom, understanding Full Nodes' role and potentially operating one is a path worth exploring.