Revealing degree distribution of bursting neuron networks.

We present a method to infer the degree distribution of a bursting neuron network from its dynamics. Burst synchronization (BS) of coupled Morris-Lecar neurons has been studied under the weak coupling condition. In the BS state, all the neurons start and end bursting almost simultaneously, while the spikes inside the burst are incoherent among the neurons. Interestingly, we find that the spike amplitude of a given neuron shows an excellent linear relationship with its degree, which makes it possible to estimate the degree distribution of the network by simple statistics of the spike amplitudes. We demonstrate the validity of this scheme on scale-free as well as small-world networks. The underlying mechanism of such a method is also briefly discussed.