The equilibrium geometries of 54 small molecules containing linear or near-linear N-H...N bonds (sample M) have been optimized at the MP2/6-31G(d,p) level and the values of p' and p" of the parameters pc at the bond-critical points (p' in the N-H, p" in the H...N bond) have been computed from the results of these optimizations. Because the N-H and the H...N part of an N-H...N bond system have different character, the trends of p' and of p" in M are described by different functions. With the pc as descriptors (the electron density rho(c), the curvatures lambda(c,i), the Laplacian del(c)(2), the kinetic energy densities G(c) and K-c, and the potential energy density V-c), we have searched for correlations of p' and p" (homocorrelations) in M. A high degree of correlation has been found for all the parameters. With the exception of the linear rho',rho" correlation the homocorrelations of the other p(c) are nonlinear and some of them nonmonotonic. The homocorrelations permit estimates of the p(c) values, p(s), in symmetric N-H-N bonds, where estimates from experiment are not without problems. They also answer some of the questions concerning limiting values of the p(c). With the exception of G(c) correlations between unlike pc's (heterocorrelations, p',q' and p",q") will be reported in a subsequent paper, now in preparation. The heterocorrelations involving G(c) are included here because of the prominence of G(c) in recent discussion of hydrogen bonds in the literature.