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.
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