We investigate the structural properties of a spatio-temporal network of earthquake events that incorporates magnitude information between the connected events.The network creates temporally directed links from an origin event towards a later event if it breaks the record closest distance from the origin among all the events in the catalog so far. Additionally, the links are conditionally classified based on the magnitude difference between connected events: “up” (“down”) connections point from a weaker (stronger) to a stronger (weaker) event. Using earthquake records from the Philippines from 1973 to 2012 and southern California from 1982 to 2012, we observe that the out-degree distributions show slight deviations from the corresponding Poisson distribution of the same mean. The space and time separations of connected earthquakes both show power-law regimes, suggesting spatio-temporal (self-)organization. More importantly, the conditional distributions of “up” and “down” connections in space, time, and network structure point to a higher likelihood of a stronger event triggering a nearby weaker event for the first few connections, as in the case of aftershocks. The results are captured by a sandpile-based model where a small but finite probability of preferentially targeting the most susceptible grid site is introduced. Our analysis, coupled with the discrete model analog, provides a quantitative picture of the spatio-temporal and magnitude organization of seismicity beyond just the successive events. The technique may be extended to further characterize similar long-period earthquake records to yield a more complete picture of the underlying processes involved in seismicity..