Branch length symmetry (BLS) entropy, defined on a simple network consisting of a single node and branches, was used to characterize facial expressions in both males and females. As a component of a larger network, this simple network is referred to as a unit branching network (UBN). We introduced a new variable, ¥ã, which represents the topological property of the network, as a function of entropy in order to topologically characterize a branching network composed of UBNs. We constructed UBNs for images of 70 male and 56 female faces displaying four different expressions (neutral, happy, angry, and screaming) by joining 17 facial landmark points such as the centers of the eyes, the corners of the mouth, and the underside tip of the nose. Based on these expressions, we computed the values of ¥ã for the facial networks and found a statistical difference between the ¥ã values of male and female faces. With the exception of a comparison between the neutral and the angry expressions, which had the same ¥ã values, there was a significant difference in the ¥ã values among different expressions within the same gender. Neutral and angry expressions had equal ¥ã values because the change in the distances between the facial landmark points for these two expressions was negligible. This study is valuable because it demonstrates that BLS entropy can be usefully applied to characterize facial expressions.