In this paper we present an unsupervised learning approach to detect meaningful job traffic patterns in Grid log data. Manual anomaly detection on modern Grid environments is troublesome given their in- creasing complexity, the distributed, dynamic topology of the network and heterogeneity of the jobs being executed. The ability to automat- ically detect meaningful events with little or no human intervention is therefore desirable. We evaluate our method on a set of log data col- lected on the Grid. Since we lack a priori knowledge of patterns that can be detected and no labelled data is available, an unsupervised learning method is followed. We cluster jobs executed on the Grid using Affinity Propagation. We try to explain discovered clusters using representative features and we label them with the help of domain experts. Finally, as a further validation step, we construct a classifier for five of the detected clusters and we use it to predict the termination status of unseen jobs.