Generating concepts defined by a binary relation between a set P of properties and a set O of objects is one of the important current problems encountered in Data Mining. We present a new algorithmic process which generates each concept exactly once, using graph-theoretic results. We present two associated algorithms, both with a good worst-time complexity analysis, which make them competitive with the best existing algorithms. This process has a time complexity of O(|P|.m) per maximal chain of the concept lattice, where m denotes the size of the complement of the relation, and uses a data structure which is of small polynomial size. Our algorithms can be used to compute the edges of the lattice as well as to generate only frequent sets.