Abstract: A graph includes nodes connected with one or more edges. Each node in the graph may be encoded in a neuron in a neural network. The neural network may include neurons arranged in a spiking neuromorphic architecture. To find the shortest path between a first node and a second node in the graph, a spike may propagate from a first neuron encoding the first node to a second neuron encoding the second node. Another spike may propagate from the second neuron to the first neuron. Each neuron spiking in a propagation may store a value that indicates the depth of the neuron in a propagation path. A spiking neuron may generate two values in the two propagations, respectively. A spiking neuron having two equal values may be identified. The shortest path includes one or more edges that connect the nodes encoded in the identified spiking neurons.