This paper introduces a dynamic graph partitioning algorithm, designed for large, constantly changing graphs. We propose a partitioning framework that adjusts on the fly as the graph structure changes. We also introduce a replication algorithm that is tightly integrated with the partitioning algorithm, which further reduces the number of edges cut by the partitioning algorithm. Even though the proposed approach is handicapped by only taking into consideration local parts of the graph when reassigning vertices, extensive evaluation shows that the proposed approach maintains a quality partitioning over time, which is comparable at any point in time to performing a full partitioning from scratch using a state-the-art static graph partitioning algorithm such as METIS. Furthermore, when vertex replication is turned on, edge-cut can improve by an order of magnitude.