Analyzing the connectome of a nervous system provides valuable information about the functions of its subsystems. Although much has been learned about the architectures of neural networks in various organisms by applying analytical tools developed for general networks, two distinct and functionally important properties of neural networks are often overlooked. First, neural networks are endowed with polarity at the circuit level: Information enters a neural network at input neurons, propagates through interneurons, and leaves via output neurons. Second, many functions of nervous systems are implemented by signal propagation through high-level pathways involving multiple and often recurrent connections rather than by the shortest paths between nodes. In the present study, we analyzed two neural networks: the somatic nervous system of Caenorhabditis elegans (C. elegans) and the partial central complex network of Drosophila, in light of these properties. Specifically, we quantified high-level propagation in the vertical and horizontal directions: the former characterizes how signals propagate from specific input nodes to specific output nodes and the latter characterizes how a signal from a specific input node is shared by all output nodes. We found that the two neural networks are characterized by very efficient vertical and horizontal propagation. In comparison, classic small-world networks show a trade-off between vertical and horizontal propagation; increasing the rewiring probability improves the efficiency of horizontal propagation but worsens the efficiency of vertical propagation. Our result provides insights into how the complex functions of natural neural networks may arise from a design that allows them to efficiently transform and combine input signals.