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www.nature.com/scientificreports/ Scientific Reports | Figure 4. Key network properties. (a) Pdf of the traders’ strength. (b) Traders’ strength as a function of the number of days of activity. (c) Percentage of transaction traders make toward their top and second-top NFT collections. (d) Pdf of the NFTs’ strength. (e) Percentage of transactions between NFTs in different collections as a function of the size of the collection. (f) Percentage of NFTs belonging to the first and second largest strong connected component (SCC). Solid curves in (b), (c), (e) and (f) represent average values, while respective bands the 95% confidence interval. is close to the null value zero, implying that traders do not connect to other traders based on the similarity of their connection patterns. Finally, we focus on the network structure. Building upon the result that traders are specialized, we assign each trader to their top collection, and we study the modularity29 of the network under this partition of nodes. The modularity is a metric bounded between −0.5 and 1, which is positive when the density of links among nodes assigned to the same partition is larger than it would be expected by chance. We find that the modular- ity Q of the collections partition is Q = 0.613, significantly higher than what expected from a random network Q = 0.0823 ± 0.0001 (see “SI”). It reveals that the collections well represent the underlining network structure, where traders specialized in a collection tends to buy and sell NFTs with other traders specialized in the same collection. We now turn to the exploration of how NFTs are connected to one another. To this end, we construct the network of NFTs, where nodes are NFTs and a directed link exists between two NFTs that are purchased “in sequence”, e.g. a link is created from an NFT to another when a buyer purchases the former and then the latter, with no purchases between the two (see “SI” for more details). Rather than linking all NFTs ever traded by the same trader, this choice allows to understand the relations between NFT that are semantically similar, because they are bought by the same trader in approximately the same period of time. Further, it ensures that the network structure is not dominated by large cliques. The distribution of NFTs strength decays as a power law with exponent 3 = −3.21 (see Fig. 4d). Note that the strength of NFTs is different to the total number of sales per NFT (previously shown in Fig. 2b), due to how the network is constructed. In fact, when two NFTs are purchased simultaneously, this creates two links for each of the two nodes (one ingoing and one outgoing). The next question we ask is: which NFTs are connected to one another? We find that NFTs in small collections tend to be bought in sequence with NFTs in other collections (see Fig. 4e). On the contrary, NFTs in large collections, like CryptoKitties or Gods-Unchained, tend to be bought in sequence with NFTs in the same collection. What are the implications of this behaviour on the NFT network structure? We investigate the relation between the structure of the NFT network and NFTs collections, by studying the modularity29 of the network under the partition of NFTs (nodes) into NFT collections. We find that the modularity Q of the collections partition is Q = 0.80, significantly higher than what expected from a random network Q = 0.1110 ± 0.0001. It reveals that (1) the network is clustered and (2) the collections well represent the underlining community structure. By further exploring the relationship between traders’ behaviour and NFT networks structure, we unveil that, while the NFT network is clustered, communities are not isolated. That is, some traders buy or sell assets belonging to multiple collections. The network of NFTs has two strongly connected components (SCC)30, defined as groups of nodes such that, starting from a given NFTs, it is possible to reach any other NFTs in the SCC following directed links. The largest SCC include NFTs traded in the WAX blockchain, consisting of 35% of all NFTs, while the second largest includes NFTs traded in the Ethereum blockchain, consisting of 20% of all NFTs (see Fig. 4f). While the high network modularity reveals that traders tend to purchase assets from the same collection in sequence, the presence of very large SCCs reveals that there are less frequent sequences of purchases in different collections. A visual representation of the trader network including the Art category on February 2021 shows the clusters formed by NFT traders specialized in the same collection (see Fig. 5a). Similarly, the same visualization for the (2021) 11:20902 | https://doi.org/10.1038/s41598-021-00053-8 5 Vol.:(0123456789)PDF Image | Mapping the NFT revolution
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