5.4.2 Network Entropy

A profound method to evaluate intricate characteristics of network evolution and their interdependencies involves the analysis of network entropy. Originating from Shannon entropy, network entropy quantifies the average measure of a network's heterogeneity, focusing on the network's degree probability distribution. Liusan Wu, in his paper (Wu, Tan, and Zhang 2013), delved into certain dimensions of how entropy impacts network efficiency.

In the sphere of the DGT Network, entropy is not just an abstract concept but an actionable metric. It quantifies the unpredictability, randomness, or intricacy present in the system. Its formulation is rooted in the proportion between the transaction count, denoted as TX, and the total nodes, represented as in the network. This ratio is termed (Probability of Transaction). An intriguing correlation emerges as entropy swells, indicating more intricate information patterns, there's a corresponding surge in value transfer, culminating in heightened token demand.

Thus, within this framework, entropy provides a lens into the system's uncertainty. For a blockchain infrastructure, an elevated entropy implies a plethora of independent transactions and diverse usage patterns. This translates to a vast, diversified network marked by an intensified value transfer.

Drawing from information theory, the entropy's computation derives from the Shannon entropy formula:

$$S_{\epsilon} = -P_{TX}^B * \log_2{P_{TX}^B} \ \ \ \ \ \ \ \tag{22}$$

Where:

• represents the likelihood of each active node initiating a transaction.
• TX stands for the transaction volume.

• signifies the count of active nodes in a given month.

By entwining both the transaction count and node count, this method offers a holistic perspective of the network's performance, emphasizing its interconnected nature. A representative curve of network entropy can be visualized in the subsequent figure. This comprehensive perspective ensures that stakeholders understand the underlying dynamism and complexities of the network, setting the stage for informed decision-making.

Figure 77 Entropy over time