5.8.2 Node Diversity in Hybrid Networks

The resilient fabric of a network often lies quietly within the nodes that sew it together. In the context of hybrid networks, like Distributed General Technologies (DGT), which harmonize the principles of both centralized and decentralized systems, understanding the role and dynamics of nodes becomes paramount. This exploration becomes particularly intriguing and multifaceted when it dips into the realm of Node Diversity.

• Independent Nodes and Their Calculative Model: Nodes, in essence, can be seen as independent or dependent, a distinction based on their managerial status within the network. The Independent Nodes, functioning autonomously and managed by individual entities, are numerically outlined by:

$$N_{independent}= U_{network} \cdot r_{ind}^{max} \cdot Nodes \ \ \ \ \ \ \ \ \tag{42}$$

In this expression, encapsulates the network's utility, signaling its appeal and functionality for entities, particularly those with restricted resources, to run independent nodes. represents the maximum ratio of independent nodes permissible in the network, ensuring a balance between autonomy and structured control within the network dynamics.

The flip side reveals Node Dependency, where nodes, instead of existing as separate entities, are operated or influenced by an overarching body or a consortium. In DGT networks, a fascinating fusion of public and private structures often results in a significant number of dependent nodes, balancing inclusivity, and operational efficacy.

Figure 94 Independent Nodes Over Time

• Consortium's Dominance: Focusing on the concept of Consortium Nodes, it becomes evident that, particularly in hybrid networks, initial control often resides significantly with a founding consortium. Their influence, while dominant initially, undergoes a gradual dissipation as more entities integrate into the network. This decentralization process is aptly governed by the "decay rate", reflecting the consortium’s relinquishing speed of control over the network.

Figure 95 Nodes controlled by the Consortium vs other nodes

• Multinode Entities: Multinode Entities, those wielding control over multiple nodes, introduce another layer to our exploration. These entities balance their interests and capabilities, affecting the distribution and control of nodes within the network. Their impact and evolution within the network are shaped by initial conditions, entity interest, time-dependent capability, node distribution, and updated entity multinodes, ensuring a dynamic and evolving node structure within the network.

Figure 96 Multinode Entities

• Quantifying Node Diversity through Indices: The complexity and multifaceted nature of node dynamics within the network beckon the necessity for quantifiable metrics. Enter the Node Diversity Index:

o Shannon Diversity Index (SDI): Capturing the essence of diversity within node distribution among independent entities, the SDI provides a quantitative insight into the network's decentralization. A higher SDI heralds a balanced distribution of nodes, promoting a healthier, more decentralized network.

Here is proportion of nodes controlled by entity in a network.

o Node Diversity Index (NDI): Offering a nuanced view, the NDI adjusts the Shannon Diversity Index to account for the total number of entities, facilitating a more comparative analysis across networks of varying sizes.

o Largest Entity Node Ratio (LE Ratio): This provides a straightforward measure of decentralization by determining the proportion of nodes controlled by the most substantial entity within the network. A lower LE Ratio insinuates a more decentralized network, paving the way for a more democratic and less monopolistic control of the network.

Through the lens of node diversity, this detailed exploration uncovers the subtle and yet crucial dynamics that fuel the robustness and operational efficacy of hybrid networks like DGT. It provides not just a peek into the existing structure but forms a foundational basis upon which future networks might be modeled, analyzed, and optimized, ensuring they are sculpted with a nuanced understanding of node dynamics and control.

Figure 97 Node Distribution Index

The dance between dependency and independence, control and freedom, forms a delicate balance that will continue to shape the future of network design and functionality in the digital realm.