NFT Networks Mirror Social Structures with Influencer Nodes, Community Hubs, & Zipfian Distributions

Author: (1) Prakhyat Khati, Computer Science, University of Saskatchewa, Saskatoon, Canada (khati.prakhyat@usask.com). Table of Links Abstract and 1 Introduction 2 Related Works 3 Datasets and Experiment Setup 4 Methodology 4.1 NFTs Transaction Network 4.2 NFTs Bubble Prediction 5 Discussion and Conclusions, and References 5. DISCUSSION AND CONCLUSIONS In this work, we investigate the NFT transaction graphs and analyze the different global network properties e.g., reciprocity, assortativity, core decomposition, and clustering coefficient, we realize how their connections change. We discussed what these network properties resemble in such a network. We observed the log rank of token owners and found it to be following Zipf’s law which is generally understood to be a power-law distribution with integer values. Many real graphs for social media and the internet show existence of (several)high degree nodes. For example, several social networks have influencer nodes, and in web networks, they are popular and high-ranked websites. These all kinds of networks have been confirmed to follow power laws in their degree distribution. We observed high influencer nodes in the network and community being formed around them, indicating single hub dominating the network. The single hub is the NFT collection owner who are frequently trading. In face in [5].it has been shown that a single hub frequently dominates individual networks for ERC-20 tokens. Article ranking was used to identify such influencer nodes and Gephi was used to plot the community formed around such nodes. This led to the conclusion that the structure of NFT network is qualitatively very similar to the one measured for interaction in social network. In the fig 12 below, overall, the LPPL model seems to capture the the trend of both the positive and negative bubble for CryptoPunks collection. In the result, although the price rose further after bubbleindicator(pos) reached its highest in late August 2020. The model is successful in predicting the direction of price change but around October 2020 to March 2021 here the bubbleindicator(pos) failed to predict the continuous price increase Similarly, from the fig 12, near December 20,2021 the bubble indicators are signaling negative value ~ 0.3. This implies that NFT collection are in general, a small bubble (predicting price increase). This study also shed quantitative light on a NFT market that might otherwise be prone to hype and misleading information. Future work Following our characterization of the NFT network, there is ample opportunity for future work. Study the nature of NFT collection, identify what distinguishes the NFTs collection and what adds on value to those collections. Identifying entropy of ownership could be one of many ways to capture utility of NFT collection. Similar Further research can be used to refine our knowledge and understand the relation between blockchain platforms and NFT collections specific to those platforms. Study the temporal nature of network community formation of NFTs and predict the nature of the communities Similarly bubble prediction of the whole NFT collection can be done. Also, in the current time-series we assumed the CryptoPunks collection to be homogeneous nature, but all these NFTs are heterogeneous. REFERENCES [1] D. Vujičić, D. Jagodić, and S. Ranđić, Blockchain technology, bitcoin, and Ethereum: A brief overview; Blockchain technology, bitcoin, and Ethereum: A brief overview. 2018. doi: 10.1109/INFOTEH.2018.8345547. [2] L. Zhao, S. sen Gupta, A. Khan, and R. Luo, “Temporal Analysis of the Entire Ethereum Blockchain Network; Temporal Analysis of the Entire Ethereum Blockchain Network,” p. 12, doi: 10.1145/3442381.3449916. [3] “NFTs: What Are You Buying and What Do You Actually Own? - The Fashion Law.” https://www.thefashionlaw.com/nfts-what-are-you-buying-and-what-doyou-actually-own/ (accessed Apr. 18, 2022). [4] “ERC-20 Token Standard | ethereum.org.” https://ethereum.org/en/developers/docs/standards/tokens/erc-20/ (accessed Apr. 18, 2022). [5] F. Victor and B. K. Lüders, “Measuring Ethereum-Based ERC20 Token Networks,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11598 LNCS, pp. 113–129, 2019, doi: 10.1007/978-3-030-32101-7_8. [6] “What is ether (ETH)? | ethereum.org.” https://ethereum.org/en/eth/ (accessed Apr. 18, 2022). [7] “ERC-721 Non-Fungible Token Standard | ethereum.org.” https://ethereum.org/en/developers/docs/standards/tokens/erc-721/#top (accessed Apr. 18, 2022). [8] L. Ante, “Non-fungible token (NFT) markets on the Ethereum blockchain: Temporal development, cointegration and interrelations,” 2021, Accessed: Apr. 18, 2022. [Online]. Available: https://ssrn.com/abstract=3904683 [9] “The Non-Fungible Token Bible: Everything you need to know about NFTs - OpenSea Blog.” https://opensea.io/blog/guides/non-fungible-tokens/ (accessed Apr. 18, 2022). [10] glayan Aksoy, “NFTs and copyright: challenges and opportunities”, doi: 10.1093/jiplp/jpab104. [11] S. Casale-Brunet, P. Ribeca, P. Doyle, and M. Mattavelli, “Networks of Ethereum Non-Fungible Tokens: A graph-based analysis of the ERC-721 ecosystem,” Institute of Electrical and Electronics Engineers Inc., 2021. doi: 10.1109/Blockchain53845.2021.00033. [12] “Top Non-Fungible Tokens (NFT) Coins by Market Capitalization - CoinGecko.” https://www.coingecko.com/en/categories/non-fungible-tokens-nft (accessed Apr. 18, 2022). [13] “NFT sales surge as speculators pile in, sceptics see bubble | Reuters.” https://www.reuters.com/technology/nft-sales-surge-speculators-pile-scepticssee-bubble-2021-08-25/ (accessed Apr. 18, 2022). [14] “Testing for financial crashes using the Log Periodic Power Law model,” 2020. [15] A. Macdonell, “Popping the Bitcoin Bubble: An application of log--periodic power law modeling to digital currency,” 2014. [16] “Ethereum wallets | ethereum.org.” https://ethereum.org/en/wallets/ (accessed Apr. 18, 2022). [17] T. Chen et al., “Understanding Ethereum via Graph Analysis,” ACM Transactions on Internet Technology, vol. 20, no. 2, 2020, doi: 10.1145/3381036. [18] W. Chen, T. Zhang, Z. Chen, Z. Zheng, and Y. Lu, “Traveling the token world: A graph analysis of Ethereum ERC20 token ecosystem,” in The Web Conference 2020 - Proceedings of the World Wide Web Conference, WWW 2020, Apr. 2020, pp. 1411–1421. doi: 10.1145/3366423.3380215. [19] S. Casale-Brunet, P. Ribeca, P. Doyle, and M. Mattavelli, “Networks of Ethereum Non-Fungible Tokens: A graph-based analysis of the ERC-721 ecosystem,” pp. 188–195, Jan. 2022, doi: 10.1109/blockchain53845.2021.00033. [20] S. Maeng, M. Essaid, C. Lee, S. Park, and H. Ju, “Visualization of Ethereum P2P network topology and peer properties,” in International Journal of Network Management, Nov. 2021, vol. 31, no. 6. doi: 10.1002/nem.2175. [21] “[PDF] O Bitcoin Where Art Thou? Insight into Large-Scale Transaction Graphs | Semantic Scholar.” https://www.semanticscholar.org/paper/O-Bitcoin-WhereArt-Thou-Insight-into-Large-Scale-HaslhoferKarl/96b95da0ab88de23641014abff2a5c0b5fec00c9 (accessed Apr. 18, 2022). [22] D. Ron and A. Shamir, “Quantitative Analysis of the Full Bitcoin Transaction Graph,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7859 LNCS, pp. 6–24, 2013, doi: 10.1007/978-3-642-39884-1_2. [23] S. Ferretti and G. D. ’ Angelo, “On the Ethereum Blockchain Structure: a Complex Networks Theory Perspective”, Accessed: Apr. 18, 2022. [Online]. Available: https://doi.org/10. [24] S. Somin, G. Gordon, and Y. Altshuler, “Network Analysis of ERC20 Tokens Trading on Ethereum Blockchain,” Springer Proceedings in Complexity, pp. 439–450, 2018, doi: 10.1007/978-3-319-96661-8_45/FIGURES/2. [25] S. Somin, G. Gordon, and Y. Altshuler, “Social Signals in the Ethereum Trading Network”. [26] F. Victor and B. K. Lüders, “Measuring Ethereum-based ERC20 Token Networks”, Accessed: Apr. 18, 2022. [Online]. Available: https://github.com/ethereum/EIPs/blob/master/EIPS/ [27] M. Nadini, L. Alessandretti, F. di Giacinto, M. Martino, L. Maria Aiello, and A. Baronchelli, “Mapping the NFT revolution: market trends, trade networks, and visual features,” Scientific Reports |, vol. 11, p. 20902, 123AD, doi: 10.1038/s41598-021-00053-8. [28] L. Ante, “The non-fungible token (NFT) market and its relationship with Bitcoin and Ethereum,” 2021, Accessed: Apr. 18, 2022. [Online]. Available: https://ssrn.com/abstract=3861106 [29] “[PDF] Evaluating Asset Bubbles within Cryptocurrencies using the LPPL Model | Semantic Scholar.” https://www.semanticscholar.org/paper/EvaluatingAsset-Bubbles-within-Cryptocurrencies-TiryakianKim/05772c539ce0cc05769f814ea10f148213b4a800 (accessed Apr. 18, 2022). [30] M. Bianchetti, “Are cryptocurrencies real financial bubbles? Evidence from quantitative analyses”. [31] J. Xiong, Q. Liu, and L. Zhao, “A new method to verify Bitcoin bubbles: Based on the production cost,” North American Journal of Economics and Finance, vol. 51, Jan. 2020, doi: 10.1016/J.NAJEF.2019.101095. [32] D. C. A. Mallqui and R. A. S. Fernandes, “Predicting the direction, maximum, minimum and closing prices of daily Bitcoin exchange rate using machine learning techniques,” Applied Soft Computing Journal, vol. 75, pp. 596–606, Feb. 2019, doi: 10.1016/J.ASOC.2018.11.038. [33] A. M. Khedr, I. Arif, P. v. Pravija Raj, M. El-Bannany, S. M. Alhashmi, and M. Sreedharan, “Cryptocurrency price prediction using traditional statistical and machine-learning techniques: A survey,” Intelligent Systems in Accounting, Finance and Management, vol. 28, no. 1, pp. 3–34, Jan. 2021, doi: 10.1002/ISAF.1488. [34] K. Ito, K. Shibano, and G. Mogi, “Predicting the Bubble of Non-Fungible Tokens (NFTs): An Empirical Investigation”, Accessed: Apr. 18, 2022. [Online]. Available: www.larvalabs.com/cryptopunks, [35] “crypto_ethereum – BigQuery – Google Cloud Platform.” https://console.cloud.google.com/bigquery?project=bigquery-publicdata&page=dataset&d=crypto_ethereum&p=bigquery-publicdata&redirect_from_classic=true&ws=!1m8!1m3!3m2!1sbigquery-publicdata!2sbitcoin_blockchain!1m3!3m2!1sbigquery-publicdata!2scrypto_ethereum (accessed Apr. 18, 2022). [36] “NonFungible.com | Analyze, track & discover NFTs and collectible art markets.” https://nonfungible.com/ (accessed Apr. 18, 2022). [37] “Ethereum Name Service.” https://ens.domains/ (accessed Apr. 19, 2022). [38] P. Geraskin and D. Fantazzini, “Munich Personal RePEc Archive Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask,” 2011. This paper is available on arxiv under CC BY 4.0 DEED license. Author: (1) Prakhyat Khati, Computer Science, University of Saskatchewa, Saskatoon, Canada (khati.prakhyat@usask.com). Author: Author: (1) Prakhyat Khati, Computer Science, University of Saskatchewa, Saskatoon, Canada (khati.prakhyat@usask.com). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2 Related Works 3 Datasets and Experiment Setup 3 Datasets and Experiment Setup 4 Methodology 4 Methodology 4.1 NFTs Transaction Network 4.1 NFTs Transaction Network 4.2 NFTs Bubble Prediction 4.2 NFTs Bubble Prediction 5 Discussion and Conclusions, and References 5 Discussion and Conclusions, and References 5. DISCUSSION AND CONCLUSIONS In this work, we investigate the NFT transaction graphs and analyze the different global network properties e.g., reciprocity, assortativity, core decomposition, and clustering coefficient, we realize how their connections change. We discussed what these network properties resemble in such a network. We observed the log rank of token owners and found it to be following Zipf’s law which is generally understood to be a power-law distribution with integer values. Many real graphs for social media and the internet show existence of (several)high degree nodes. For example, several social networks have influencer nodes, and in web networks, they are popular and high-ranked websites. These all kinds of networks have been confirmed to follow power laws in their degree distribution. We observed high influencer nodes in the network and community being formed around them, indicating single hub dominating the network. The single hub is the NFT collection owner who are frequently trading. In face in [5].it has been shown that a single hub frequently dominates individual networks for ERC-20 tokens. Article ranking was used to identify such influencer nodes and Gephi was used to plot the community formed around such nodes. This led to the conclusion that the structure of NFT network is qualitatively very similar to the one measured for interaction in social network. In the fig 12 below, overall, the LPPL model seems to capture the the trend of both the positive and negative bubble for CryptoPunks collection. In the result, although the price rose further after bubbleindicator(pos) reached its highest in late August 2020. The model is successful in predicting the direction of price change but around October 2020 to March 2021 here the bubbleindicator(pos) failed to predict the continuous price increase Similarly, from the fig 12, near December 20,2021 the bubble indicators are signaling negative value ~ 0.3. This implies that NFT collection are in general, a small bubble (predicting price increase). This study also shed quantitative light on a NFT market that might otherwise be prone to hype and misleading information. Future work Future work Following our characterization of the NFT network, there is ample opportunity for future work. Study the nature of NFT collection, identify what distinguishes the NFTs collection and what adds on value to those collections. Identifying entropy of ownership could be one of many ways to capture utility of NFT collection. Similar Further research can be used to refine our knowledge and understand the relation between blockchain platforms and NFT collections specific to those platforms. Study the temporal nature of network community formation of NFTs and predict the nature of the communities Similarly bubble prediction of the whole NFT collection can be done. Also, in the current time-series we assumed the CryptoPunks collection to be homogeneous nature, but all these NFTs are heterogeneous. REFERENCES [1] D. Vujičić, D. Jagodić, and S. Ranđić, Blockchain technology, bitcoin, and Ethereum: A brief overview; Blockchain technology, bitcoin, and Ethereum: A brief overview. 2018. doi: 10.1109/INFOTEH.2018.8345547. [2] L. Zhao, S. sen Gupta, A. Khan, and R. Luo, “Temporal Analysis of the Entire Ethereum Blockchain Network; Temporal Analysis of the Entire Ethereum Blockchain Network,” p. 12, doi: 10.1145/3442381.3449916. [3] “NFTs: What Are You Buying and What Do You Actually Own? - The Fashion Law.” https://www.thefashionlaw.com/nfts-what-are-you-buying-and-what-doyou-actually-own/ (accessed Apr. 18, 2022). [4] “ERC-20 Token Standard | ethereum.org.” https://ethereum.org/en/developers/docs/standards/tokens/erc-20/ (accessed Apr. 18, 2022). [5] F. Victor and B. K. Lüders, “Measuring Ethereum-Based ERC20 Token Networks,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11598 LNCS, pp. 113–129, 2019, doi: 10.1007/978-3-030-32101-7_8. [6] “What is ether (ETH)? | ethereum.org.” https://ethereum.org/en/eth/ (accessed Apr. 18, 2022). [7] “ERC-721 Non-Fungible Token Standard | ethereum.org.” https://ethereum.org/en/developers/docs/standards/tokens/erc-721/#top (accessed Apr. 18, 2022). [8] L. Ante, “Non-fungible token (NFT) markets on the Ethereum blockchain: Temporal development, cointegration and interrelations,” 2021, Accessed: Apr. 18, 2022. [Online]. Available: https://ssrn.com/abstract=3904683 [9] “The Non-Fungible Token Bible: Everything you need to know about NFTs - OpenSea Blog.” https://opensea.io/blog/guides/non-fungible-tokens/ (accessed Apr. 18, 2022). [10] glayan Aksoy, “NFTs and copyright: challenges and opportunities”, doi: 10.1093/jiplp/jpab104. [11] S. Casale-Brunet, P. Ribeca, P. Doyle, and M. Mattavelli, “Networks of Ethereum Non-Fungible Tokens: A graph-based analysis of the ERC-721 ecosystem,” Institute of Electrical and Electronics Engineers Inc., 2021. doi: 10.1109/Blockchain53845.2021.00033. [12] “Top Non-Fungible Tokens (NFT) Coins by Market Capitalization - CoinGecko.” https://www.coingecko.com/en/categories/non-fungible-tokens-nft (accessed Apr. 18, 2022). [13] “NFT sales surge as speculators pile in, sceptics see bubble | Reuters.” https://www.reuters.com/technology/nft-sales-surge-speculators-pile-scepticssee-bubble-2021-08-25/ (accessed Apr. 18, 2022). [14] “Testing for financial crashes using the Log Periodic Power Law model,” 2020. [15] A. Macdonell, “Popping the Bitcoin Bubble: An application of log--periodic power law modeling to digital currency,” 2014. [16] “Ethereum wallets | ethereum.org.” https://ethereum.org/en/wallets/ (accessed Apr. 18, 2022). [17] T. Chen et al., “Understanding Ethereum via Graph Analysis,” ACM Transactions on Internet Technology, vol. 20, no. 2, 2020, doi: 10.1145/3381036. [18] W. Chen, T. Zhang, Z. Chen, Z. Zheng, and Y. Lu, “Traveling the token world: A graph analysis of Ethereum ERC20 token ecosystem,” in The Web Conference 2020 - Proceedings of the World Wide Web Conference, WWW 2020, Apr. 2020, pp. 1411–1421. doi: 10.1145/3366423.3380215. [19] S. Casale-Brunet, P. Ribeca, P. Doyle, and M. Mattavelli, “Networks of Ethereum Non-Fungible Tokens: A graph-based analysis of the ERC-721 ecosystem,” pp. 188–195, Jan. 2022, doi: 10.1109/blockchain53845.2021.00033. [20] S. Maeng, M. Essaid, C. Lee, S. Park, and H. Ju, “Visualization of Ethereum P2P network topology and peer properties,” in International Journal of Network Management, Nov. 2021, vol. 31, no. 6. doi: 10.1002/nem.2175. [21] “[PDF] O Bitcoin Where Art Thou? Insight into Large-Scale Transaction Graphs | Semantic Scholar.” https://www.semanticscholar.org/paper/O-Bitcoin-WhereArt-Thou-Insight-into-Large-Scale-HaslhoferKarl/96b95da0ab88de23641014abff2a5c0b5fec00c9 (accessed Apr. 18, 2022). [22] D. Ron and A. Shamir, “Quantitative Analysis of the Full Bitcoin Transaction Graph,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7859 LNCS, pp. 6–24, 2013, doi: 10.1007/978-3-642-39884-1_2. [23] S. Ferretti and G. D. ’ Angelo, “On the Ethereum Blockchain Structure: a Complex Networks Theory Perspective”, Accessed: Apr. 18, 2022. [Online]. Available: https://doi.org/10. [24] S. Somin, G. Gordon, and Y. Altshuler, “Network Analysis of ERC20 Tokens Trading on Ethereum Blockchain,” Springer Proceedings in Complexity, pp. 439–450, 2018, doi: 10.1007/978-3-319-96661-8_45/FIGURES/2. [25] S. Somin, G. Gordon, and Y. Altshuler, “Social Signals in the Ethereum Trading Network”. [26] F. Victor and B. K. Lüders, “Measuring Ethereum-based ERC20 Token Networks”, Accessed: Apr. 18, 2022. [Online]. Available: https://github.com/ethereum/EIPs/blob/master/EIPS/ [27] M. Nadini, L. Alessandretti, F. di Giacinto, M. Martino, L. Maria Aiello, and A. Baronchelli, “Mapping the NFT revolution: market trends, trade networks, and visual features,” Scientific Reports |, vol. 11, p. 20902, 123AD, doi: 10.1038/s41598-021-00053-8. [28] L. Ante, “The non-fungible token (NFT) market and its relationship with Bitcoin and Ethereum,” 2021, Accessed: Apr. 18, 2022. [Online]. Available: https://ssrn.com/abstract=3861106 [29] “[PDF] Evaluating Asset Bubbles within Cryptocurrencies using the LPPL Model | Semantic Scholar.” https://www.semanticscholar.org/paper/EvaluatingAsset-Bubbles-within-Cryptocurrencies-TiryakianKim/05772c539ce0cc05769f814ea10f148213b4a800 (accessed Apr. 18, 2022). [30] M. Bianchetti, “Are cryptocurrencies real financial bubbles? Evidence from quantitative analyses”. [31] J. Xiong, Q. Liu, and L. Zhao, “A new method to verify Bitcoin bubbles: Based on the production cost,” North American Journal of Economics and Finance, vol. 51, Jan. 2020, doi: 10.1016/J.NAJEF.2019.101095. [32] D. C. A. Mallqui and R. A. S. Fernandes, “Predicting the direction, maximum, minimum and closing prices of daily Bitcoin exchange rate using machine learning techniques,” Applied Soft Computing Journal, vol. 75, pp. 596–606, Feb. 2019, doi: 10.1016/J.ASOC.2018.11.038. [33] A. M. Khedr, I. Arif, P. v. Pravija Raj, M. El-Bannany, S. M. Alhashmi, and M. Sreedharan, “Cryptocurrency price prediction using traditional statistical and machine-learning techniques: A survey,” Intelligent Systems in Accounting, Finance and Management, vol. 28, no. 1, pp. 3–34, Jan. 2021, doi: 10.1002/ISAF.1488. [34] K. Ito, K. Shibano, and G. Mogi, “Predicting the Bubble of Non-Fungible Tokens (NFTs): An Empirical Investigation”, Accessed: Apr. 18, 2022. [Online]. Available: www.larvalabs.com/cryptopunks, [35] “crypto_ethereum – BigQuery – Google Cloud Platform.” https://console.cloud.google.com/bigquery?project=bigquery-publicdata&page=dataset&d=crypto_ethereum&p=bigquery-publicdata&redirect_from_classic=true&ws=!1m8!1m3!3m2!1sbigquery-publicdata!2sbitcoin_blockchain!1m3!3m2!1sbigquery-publicdata!2scrypto_ethereum (accessed Apr. 18, 2022). [36] “NonFungible.com | Analyze, track & discover NFTs and collectible art markets.” https://nonfungible.com/ (accessed Apr. 18, 2022). [37] “Ethereum Name Service.” https://ens.domains/ (accessed Apr. 19, 2022). [38] P. Geraskin and D. Fantazzini, “Munich Personal RePEc Archive Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask,” 2011. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv