By considering the eigen-ratio of the normalized Laplacian matrix as a synchronizability measure, two different formulas are proposed for selecting edge weights in networks of coupled chaotic dynamical systems to enhance their synchronizability using only node betweenness centrality, where one results in a symmetric Laplacian for undirected graphs and the other results in an asymmetric Laplacian. These formulas are applied to different examples of undirected networks including small-world (SW) and scale-free (SF) networks of various sizes, and are compared with other well-known weighting procedures in the literature.