Core–periphery organization of the cryptocurrency market inferred by the modularity operator

Modularity matrix has long been used for inferring modular structure of stochastic networks of different scale-free nature. In this paper we show efficiency of the modularity to detect the core–periphery organization on the example of the cryptocurrency correlation-based network. The cryptocurrencies exemplify assets with dual macroeconomical background sharing properties of currency and stock markets with a non-obvious topological organization. We demonstrate that the modularity operator applied to a daily correlation-based network rules out community structure of the cryptocurrency market, simultaneously revealing stratification into a core and a periphery. Classification of tokens into two groups is shown to be day-dependent, however, stable tokens with statistically significant participation ratio can be easily identified. To approve the core–periphery organization of the stable assets, we compute the centrality measure of the two groups and show that it is considerably less for the periphery than for the core. Embedding of a subgraph of the stable tokens into the Euclidean space demonstrates clear spatial core–shell segregation. Furthermore, we show that the degree distribution of the minimal spanning tree has a distinctive power-law tail with exponent γ≈−2.6 which makes the cryptomarket an archetypal example of the scale-free network. Economical reasoning suggests that the revealed topological motif is in the full agreement with the outliers hypothesis. The core is driven by traditionally liquid and highly capitalized tokens, resembling blockchain and payment systems, while the periphery is marked by the stable tokens with little exposure to the market. We report that the very center of the core is populated by tokens with strong financial usage, while main drivers of the market (such as ETH or XRP) turn out to locate in the middle layers. This is an clear evidence of speculative processes underlying formation and evolution of the market.