Abstract
Typical analyses of the network architecture focus on the shortest path. However, the approach may not fully characterize the features of neural networks in at least two ways: a) A neural network has a specific direction of information flow. b) The neural pathways via multiple synaptic connections may be functionally more important than the shortest pathways. To address the issues, we measures two novel quantities: a) Vertical propagation is how quickly the main information pathway are established between input and output nodes. b) Horizontal propagation is how quickly the information from input neurons could propagate to multiple output neurons. We analysed the C. Elegans neural network, protocerebral bridge network in Drosophila, and, as comparison, artificially generated regular, small-world and random networks. Our results show that the C. Elegans and PCB neural networks are more efficient in both vertical and horizontal propagation than the small-world networks. Further analysis show that different hubs could improve the different propagation efficiency in small-world networks: provincial hubs enhance vertical propagation, kinless hubs improve horizontal propagation, and connector hubs increase the efficiency of the both propagations. In addition, this result could be supported by lesioning hubs in the C. Elegans neural network. Our results suggest that the various hubs may play different important roles in information propagations of the neural networks, and our works may deliver insight into the functions of the interneurons in primary sensory systems.