Synchronization from Second Order Network Connectivity Statistics

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks (SONETs), which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by a pool and redistribute mechanism. The pooling of many inputs averages out independent fluctuations, amplifying weak correlations in the inputs. With increased chain connections, neurons with many inputs tend to have many outputs. Hence, chains ensure that the amplified correlations in the neurons with many inputs are redistributed throughout the network, enhancing the development of synchrony across the network.