Partitioning large graphs is difficult, especially when performed in the limited models of computation afforded to modern large scale computing systems. In this work we introduce restreaming graph partitioning and develop algorithms that scale similarly to streaming partitioning algorithms yet empirically perform as well as fully offline algorithms. In streaming partitioning, graphs are partitioned serially in a single pass. Restreaming partitioning is motivated by scenarios where approximately the same dataset is routinely streamed, making it possible to transform streaming partitioning algorithms into an iterative procedure. This combination of simplicity and powerful performance allows restreaming algorithms to be easily adapted to efficiently tackle more challenging partitioning objectives. In particular, we consider the problem of stratified graph partitioning, where each of many node attribute strata are balanced simultaneously. As such, stratified partitioning is well suited for the study of network effects on social networks, where it is desirable to isolate disjoint dense subgraphs with representative user demographics. To demonstrate, we partition a large social network such that each partition exhibits the same degree distribution in the original graph -A novel achievement for non-regular graphs. As part of our results, we also observe a fundamental difference in the ease with which social graphs are partitioned when compared to web graphs. Namely, the modular structure of web graphs appears to motivate full offline optimization, whereas the locally dense structure of social graphs precludes significant gains from global manipulations.