In graph signal processing (GSP), graph learning is concerned with the inference of an underlying graph best capable of modeling a dataset of graph signals. However, more complex datasets are derived from multiple underlying graphs. In such instances, it is necessary to learn multiple graph structures, each corresponding to the graph signals residing on the same structure. In other words, the graph signals need to be partitioned into a set of clusters, with a designated topology for each cluster. In this letter, inspired from classical K-means, a new algorithm for multiple graph learning, called K-graphs, is proposed. Numerical experiments demonstrate the high performance of this algorithm, in both graph learning and data clustering.