Pore connectivity is a measure of the fraction of pore space (vesicles, voids or cracks) in a material that is interconnected on the system length scale. Pore connectivity is fundamentally related to permeability, which has been shown to control magma outgassing and the explosive potential of magma during ascent in the shallowest part of the crust. Here, we compile a database of connectivity and porosity from published sources and supplement this with additional measurements, using natural volcanic rocks produced in a broad range of eruptive styles and with a range of bulk composition. The database comprises 2715 pairs of connectivity C and porosity ϕ values for rocks from 35 volcanoes as well as 116 products of experimental work. For 535 volcanic rock samples, the permeability k was also measured. Data from experimental studies constrain the general features of the relationship between C and ϕ associated with both vesiculation and densification processes, which can then be used to interpret natural data. To a first order, we show that a suite of rocks originating from effusive eruptive behaviour can be distinguished from rocks originating from explosive eruptive behaviour using C and ϕ. We observe that on this basis, a particularly clear distinction can be made between scoria formed in fire-fountains and that formed in Strombolian activity. With increasing ϕ , the onset of connectivity occurs at the percolation threshold ϕcϕc which in turn can be hugely variable. We demonstrate that C is an excellent metric for constraining ϕcϕc in suites of porous rocks formed in a common process and discuss the range of ϕcϕc values recorded in volcanic rocks. The percolation threshold is key to understanding the onset of permeability, outgassing and compaction in shallow magmas. We show that this threshold is dramatically different in rocks formed during densification processes than in rocks formed in vesiculating processes and propose that this value is the biggest factor in controlling the evolution of permeability at porosities above ϕcϕc.