Wiring cost in the organization of a biological neuronal network

To find out the role of the wiring cost in the organization of the neuronal network of the nematode Caenorhabditis elegans, we build the spatial neuronal map of C. elegans based on geometrical positions of neurons. We show that the number of interneuronal connections of the Euclidean length d decays exponentially with d, implying that the wiring cost, defined as the sum of the interneuronal distances, plays an important role in the actual neuronal network. Using the two methods to shuffle the neuronal network in systematic ways, the edge exchange and the vertex swapping, we show that positions of neurons are not randomly distributed but organized to reduce the wiring cost. Furthermore, we discuss the trade-off between the wiring cost and the performance of the network.