Social network analysis has often been applied to criminal groups to understand their internal structure and dynamics. While the content of communications is often restricted by constitutional and procedural constraints, data about communications is often more readily accessible. This article applies advanced network analysis techniques based on spectral embedding to such traffic data. Spectral embedding facilitates deeper analysis by embedding the graph representing a social network in a geometric space such that Euclidean distance reflects pairwise node dissimilarity. This enables visualizing a network in ways that accurately reflect the structure of the underlying group, and computing properties directly from the embedding. We illustrate spectral approaches for two ‘Ndrangheta drug-smuggling networks, and extend them to a) examine triad structure (through the identification of the Simmelian backbone), which elicits key members, and b) to display temporal properties, which illustrates changing group structure. Although the two groups have the same purpose and come from the same criminal milieu, they have substantially different internal structure which was not detectable using conventional social-network approaches. The techniques presented in this study may support law enforcement in the early stages of an investigation.