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• A new basis for presenting illustrations of spatial dependence related to extreme rain. • Extreme rainfall spatial connectivity increases under ENSO phases. • RC weakens at warmer temperatures, with localized lower relative connectivity. The frequency and severity of extreme weather events have been noted to be changing in both time and space as a result of rising global temperatures. In this regard, the analysis of joint occurrences of extreme climate events has gained considerable importance for planning and emergency management as such events often result in system failures that extend beyond a single location in the region impacted. By their very definition, extremes cannot be sampled frequently, necessitating approaches that are robust and efficient and can take advantage of the Big Data movement we are now a part of. This study introduces a new concept for characterizing such dependence, termed relative connectivity, formulated using the theory of empirical copulas which represent a non-parametric method to describe the joint dependence of random variables. The spatial relative connectivity of extreme rainfall events across 2,708 rainfall stations in Australia is ascertained and conclusions drawn. The extreme rainfall events in Western Australia, southeast South Australia, and southwest Victoria exhibit higher relative connectivity than other regions, suggesting a stronger spatial dependence and higher possibility of concurrence when compared to other regions. The overall variation of relative connectivity is also examined under different low-frequency climatic anomalies (i.e. El Nino and La Nina events) and temperature states. We observe that spatial dependence across raingauges increases under both El Nino and La Nina periods, while it weakens at warmer temperatures, with localized lower relative connectivity at target raingauges. [ABSTRACT FROM AUTHOR]