While recent algorithms for mining the frequent subgraphs of a database are efficient in the general case, these algorithms tend to do poorly on databases that have a few or no labels. Although little attention has been given to such datasets, there are many existing applications which deal with this type of data. In this paper, we present a novel algorithm, called SyGMA, that improves frequent subgraph mining in such cases by limiting the impact of symmetry on calculations, without the use of memory-expensive structures. Through experimentation on various datasets, we show that our algorithm outperforms, in many cases, one of the leading algorithms for this task.