In mathematics, the hafnian of an adjacency matrix of a graph is the number of perfect matchings in the graph. It was so named by Eduardo R. Caianiello "to mark the fruitful period of stay in Copenhagen (Hafnia in Latin)." The hafnian of a symmetric matrix is computed as where is the symmetric group on . Equivalently, where is the set of all 1-factors (perfect matchings) on the complete graph , namely the set of all ways to partition the set into subsets of size . The permanent and the hafnian are related as .