1. A computer-implemented method for using event-correlation graphs to detect attacks on computing systems, at least a portion of the method being performed by a computing device comprising at least one physical processor, the method comprising: detecting a suspicious event involving a first actor within a computing system, wherein the suspicious event could not be individually classified as definitively malicious; constructing, in response to detecting the suspicious event involving the first actor, an event-correlation graph, wherein: the event-correlation graph comprises at least: a first node that represents the first actor; a second node that represents a second actor; an edge that: interconnects the first node and the second node; represents an additional suspicious event involving the first actor and the second actor; the additional suspicious event could not be individually classified as definitively malicious; each suspicious event represented in the event-correlation graph could not be individually classified as definitively malicious; calculating, based at least in part on the additional suspicious event involving the first actor and the second actor, an attack score for the event-correlation graph; determining that the attack score is greater than a predetermined threshold; determining, based at least in part on the attack score being greater than the predetermined threshold, that the suspicious event comprises an attack on the computing system, wherein the step of constructing the event-correlation graph is performed by the computing device.