5.8.4 Integral Calculation of Decentralization Metric

Ensuring decentralization in a blockchain network is pivotal to safeguarding it against single points of failure and maintaining a democratic, transparent, and secure system. The Decentralization Metric, denoted as , is meticulously designed to encapsulate the diverse facets of decentralization within a network. Comprising an amalgamation of multiple individual metrics, it provides a comprehensive, albeit simplified, view of the overall decentralization status of the system.

Constituent Indices of the Metric:

• Token Distribution Index (TDI): Reflects the equity in token holdings among network participants. A lower TDI, signaling more equitable distribution, tends to indicate enhanced decentralization.

• Node Diversity Index (NDI): Represents diversity in active nodes, where a lower NDI, suggesting widespread and varied node participation, indicates higher decentralization.

• Consortium Influence Index (CII): Quantifies the influence wielded by a consortium or a centralized entity. Lower CII values indicate reduced consortium influence, hinting at a more decentralized setup.

• Active Node Index (ANI): Denotes the percentage of nodes actively contributing to the network. A higher ANI is suggestive of elevated decentralization due to increased node activity

The formulation of integrates these indices, assimilating them into a single, expressive metric. The mathematical representation is as follows:

Here, represent the weights assigned to each constituent index, embodying their respective significance in calculating . These weights should be assigned based on the specificities of the network and the relative importance of each index within the context of the desired decentralization characteristics.

Figure 106 Decentralization Metric Over Time