We investigate the interaction between large banks and the financial sector in Europe using the cross-quantilogram approach of Han et al. (2016). We find evidence of asymmetry in the character of the spillovers between the largest European banks and the European financial sector that are dependent on the market state. Specifically, in bearish markets, the financial sector spillovers on large banks, whereas the reverse occurs during bullish markets. The time-varying analysis confirms the asymmetric character of the network structure.