Papers associated with Bitcoin and related topics in law: Part XI

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This article was first published on Dr. Craig Wright’s blog, and we republished with permission from the author. Read Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, and Part 10.

Measuring the distance between nodes has been considered complex (Chen et al., 2020) and liable to error or listed computational processing. Because of the problems with measuring networks, some authors have merely captured and produced representations of a graph network, without analyzing the impact of power and the influence of each node. A limited approach of this form has been conducted on the Ethereum network, providing a model of computer systems on the network (Kim et al., 2018); yet, such an approach fails to distinguish the validity of each node or its influence on other parts of the network.

Fei (2018) solves some problems of analyzing network influence left unaddressed by other authors, such as Kim et al. (2018). The novel approach to identifying influential nodes in complex networks also summarizes other existing centrality measures, and provides a means to capture the intensity and mutual attraction that may exist between nodes on a distributed network such as Bitcoin. Through such a process, the author delivers a means of comparing the influence of each node, allowing researchers to analyze the comparative power or effect that each system maintains.

Through such an analysis, Fei (2018) provides a means to isolate the central systems and network factors that form giant-node components within complex networks, while Chen et al. (2020) discuss automated machine-learning technologies that can simplify some of the tasks. Unfortunately, many authors, including Kim et al. (2018), continue to focus on the volume of nodes, ignoring the individual effect that more influential nodes have over the rest of the network.

Annotated Bibliography

Chen, D., Lin, Y., Li, W., Li, P., Zhou, J., & Sun, X. (2020). Measuring and Relieving the Over-Smoothing Problem for Graph Neural Networks from the Topological View. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04), 3438–3445. https://doi.org/10.1609/aaai.v34i04.5747

Chen et al. (2020) introduce the concept of graph neural networks (GNNs) as a machine-learning model connected to graph representation. The methodology integrates the mean absolute deviation (MAD) and smoothness features of many other neural networks and related machine-learning tools. The functionality also allows for the capture of network data through an automated process with a toolset known as an adaptive edge optimization system. Finally, the topography measures are analysed for noise and over-smoothing.

The primary benefit of the paper lies in the systematic and quantitative analysis of issues faced by GNNs and the optimization of systems that analyze and capture graph topographies. The analysis is done on various Pubmed and related public citation networks, and the focus has been on pruning and capturing important information between systems that are not naturally grasped and represented as such.

Fei, L., Zhang, Q., & Deng, Y. (2018). Identifying influential nodes in complex networks based on the inverse-square law. Physica A: Statistical Mechanics and Its Applications, 512, 1044–1059. https://doi.org/10.1016/j.physa.2018.08.135

Fei et al. (2018) document the process associated with identifying influential nodes in complex networks. By determining the nodes that hold the most sway and are essential in transmitting and broadcasting traffic, an analysis of decentralization and the interconnectivity between systems will be possible. The paper starts by addressing the various types of centrality measures that already exist, documenting the algorithm shortcomings and limitations. Then, the authors propose using an inverse-square law to form an index of mutual attraction between nodes in a complex network.

The paper presents a series of experiments and simulations comparing the proposed centrality measure against existing measurements such as closeness centrality, degree centrality, and eigenvector centrality. In addition, methods used with web-based systems such as Google (NASDAQ: GOOGL) in page rank and leader rank are also analyzed. Finally, the model and process extend to looking at epidemiological systems, including susceptible, infected models. The experimental validation demonstrates good statistical power in the proposed methodology.

Kim, S. K., Ma, Z., Murali, S., Mason, J., Miller, A., & Bailey, M. (2018). Measuring Ethereum Network Peers. Proceedings of the Internet Measurement Conference 2018, 91–104. https://doi.org/10.1145/3278532.3278542

Kim et al. (2018) propose a methodology for measuring network peers in the Ethereum network. The paper begins by introducing and documenting the ‘smart contract’ capability of Ethereum, and refers to the system as a ‘cryptocurrency.’ Then, the argument is presented that Ethereum is the first Turing-complete blockchain system, ignoring the capabilities within Bitcoin. The method is based on the discovery of nodes, and is deployed using a developed tool called NodeFinder. The authors claim that the tool has found over 10,000 nodes by exploring Ethereum’s P2P ecosystem.

No analysis of the node functionality, such as the development of blocks, is provided, and the measurement and validation focus on finding all participants in the system. The argument is presented that the tool is validated through external measurements where the node finds other systems that are part of the peer ecosystem. Unfortunately, no information concerning the creation of blocks has been published. Likewise, no information concerning the broadcast or transmission of either blocks or transactions is included in the study. Consequently, the analysis of “non-productive peers” (2018, p. 99) provides little benefit. In addition, as the authors have not differentiated between nodes that are clients of the network and nodes that are actively producing blocks and transmitting information, the overall value of the paper is limited.

Additional References
Chen, D., Lin, Y., Li, W., Li, P., Zhou, J., & Sun, X. (2020). Measuring and Relieving the Over-Smoothing Problem for Graph Neural Networks from the Topological View. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04), 3438–3445. https://doi.org/10.1609/aaai.v34i04.5747
Fei, L., Zhang, Q., & Deng, Y. (2018). Identifying influential nodes in complex networks based on the inverse-square law. Physica A: Statistical Mechanics and Its Applications, 512, 1044–1059. https://doi.org/10.1016/j.physa.2018.08.135
Kim, S. K., Ma, Z., Murali, S., Mason, J., Miller, A., & Bailey, M. (2018). Measuring Ethereum Network Peers. Proceedings of the Internet Measurement Conference 2018, 91–104. https://doi.org/10.1145/3278532.3278542

This article was lightly edited for clarity purposes.

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