I would define it as any trade that, under the assumption of a complete market, could be recast as an arb via trades in Arrow-Debreau securities.
A complete market is one for which Arrow-Debreau securities can be traded transaction-cost free (at mid) on all possible future states. Actual complete markets may not exist, but the SPX complex comes reasonably close.
Jarrow and Protter proved the equivalence of edge and arb in 2010 (but had been circulating in preprint for years prior, proof might also require a representative agent). To quote from the paper: "a non-zero ... alpha represents an arbitrage."
Arrow-Debreau rearrangement can be approximated (with trans cost frictions) with listed options. You've seen screen-grabs of this kind of structure here on ET multiple times. E.g. a ****-edge large enough (exceeds a certain metric level) can be recast as a ****-arb. You also see this type of rearrangment in the inverse strike squared weighting that's used in hedging/replicating var swaps. Note that the gamma curve is the RND shifted slightly right (not exactly, but more or less). The weighting turns it close to a uniform density (divide by the integral so that it integrates to unity) -- it looks like a kernel density estimate of a uniform, using a gamma or some other right-skewed positive support kernel.
Under this arrangement, there will be edges available as long as the Q-measure implied density differs from the rationally-expected P-measure density. This will happen as long as traders/investors remain risk-averse. These edges will not be traded away as they are compensation for perceived risk.