"Reachability queries acquire a new level of complexity when launched on temporal graphs, i.e. graphs in which edges and vertices have start and end times and queries may pertain to time points or in- tervals in the past. A variety of temporal reachability queries arise on such graphs. We present the first attempt to compile several natural temporal query patterns and propose a unified method called ARROW for answering them. ARROW is an “index-free” method that works by conducting multiple random walks of fixed length at query time. Being index-free ARROW is particularly well suited for applications where the temporal graph is undergoing rapid updates, such as social networks for example. ARROW’s major advantages over existing methods for temporal reachability are: it is incremental, has a negligible additional memory usage, and it can be used on a diverse set of temporal reachability queries."