 Eric W. <unk> conjectured , and McKay et al . ( 2004 ) proved , that the same numbers count the ( 0 @,@ 1 ) matrices for which all <unk> are positive real numbers . The proof is <unk> : a matrix A is an <unk> matrix of a DAG if and only if A + I is a ( 0 @,@ 1 ) matrix with all <unk> positive , where I denotes the identity matrix . Because a DAG cannot have self @-@ loops , its <unk> matrix must have a zero diagonal , so adding I preserves the property that all matrix <unk> are 0 or 1 . 
