Cryptocurrency markets are prone to violent, synchronised drawdowns, challenging the claim that a basket of crypto-assets offers genuine internal diversification. Because standard covariance-based metrics fail to capture asymptotic tail dependence, they systematically understate systemic risk and overstate diversification benefits precisely when markets crash. This study maps the conditional dependence structure of the cryptocurrency market directly in the joint tails, isolating direct extremal linkages from those mediated by the rest of the system. We analyse the daily returns of the thirteen largest cryptocurrencies over a sequence of 89 overlapping windows spanning late 2021 to 2025. We apply dynamic Hüsler-Reiss graphical models of extremes, estimated separately for joint crashes and rallies, and benchmark them against a Gaussian graphical model of ordinary co-movement. The results reveal a near-complete and stable lower-tail graph, an upper tail that thins over time to re-form sectoral structures, and the dissolution of ordinary token categories into a single block anchored by a Bitcoin-Ethereum core. These findings imply that intra-crypto diversification fails on the downside, standard risk models underestimate market-wide crash probabilities by roughly eight-fold, and dynamic extremal graphs offer a superior tool for systemic risk monitoring.
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