An Intrusion Detection System (IDS) to secure computer networks reports indicators for an attack as alerts. However, every attack can result in a multitude of IDS alerts that need to be correlated to see the full picture of the attack. In this paper, we present a correlation approach that transforms clusters of alerts into a graph structure on which we compute signatures of network motifs to characterize these clusters. A motif representation of attack characteristics is magnitudes smaller than the original alert data, but still allows to efficiently compare and correlate attacks with each other and with reference signatures. This allows not only to identify known attack scenarios, e.g., DDoS, scan, and worm attacks, but also to derive new reference signatures for unknown scenarios. Our results indicate a reliable identification of scenarios, even when attacks differ in size and at least slightly in their characteristics. Applied on real-world alert data, our approach can classify and assign attack scenarios of up to 96% of all attacks and can represent their characteristics using 1% of the size of the full alert data.