This paper revisits the topic of natural gas market integration across Europe. Against the backdrop of three EU gas directives aimed at creating competition and strengthening market connections, and the move towards hub trading and gas-on-gas pricing in the European markets, we adopt and extend the spillovers index due to Diebold and Yilmaz (2009) to examine the path of market connectivity over the period between 2005:7–2018:12. An initial estimation uncovers what might be deemed a ‘clunky’ evolution in the spillover index. We identify the cause of this, and devise a tilted ‘importance weighting based resampling’ rolling window estimation strategy which preserves the underlying evolutionary trend without overly weighting the importance of historic outliers. Our results show that although there are periods of deterioration, the level of market connectivity recovers, producing a generally increasing trend of market integration in our sample period. The connectivity index peaks at around65%, i.e. a little above halfway through to full connectivity. We conclude that the European natural gas market has achieved a non-trivial, albeit not full, level of integration to-date.