Spectral embedding for dynamic social networks

The interactions in real-world social networks change over time. Dynamic social network analysis aims to understand the structures in networks as they evolve, building on static analysis techniques but including variation. Working directly with the graphs that represent social networks is difficult, and it has become common to use spectral techniques that embed graphs in a geometry and then work with the geometry instead. We extend such spectral techniques to dynamically changing data by binding network snapshots at different times into a single directed graph structure in a way that keeps structures aligned. This global network can then be embedded. Pairwise similarity, as well as community and cluster structures can be tracked over time, and the idea of the trajectory of a node across time becomes meaningful. We illustrate the approach using a real-world dataset, the Caviar drug-trafficking network.