European Union Emission Trading System (EU ETS) is a key instrument of EU’s climate policy and the largest international cap-and-trade system. Every allowance transaction is recorded in an electronic registry, called European Union Transaction Log (EUTL). Utilizing the vast amount of EUTL data, we exploit the EU ETS transaction network as a means for understanding in depth the allowance market structure. We observe that the network follows the core-periphery structure and identify a small subset of core transactors. We provide strong evidence that despite its small size, the part of the network built around core transactors captures all the key properties of the entire EU ETS transactions network. Moreover, due to high and more regular trading, the transactions of the core members lack the “noisy” behaviour typically appearing in the periphery. Through extensive evaluation, we demonstrate that the core transactions can provide better results in explaining and forecasting the allowance price. Our work provides a compact and useful tool which can be used not only towards understanding a large and complex allowance market, but also towards evaluating one of the most prominent environmental policy instruments, the EU ETS.