The authors consider networks of pulse-coupled oscillators (neurons) with delayed interactions and complicated network connectivity, for which they investigate the problem of neuronal synchronization. They use the Mirollo-Strogatz phase representation of individual units to analyze finite networks of arbitrary connectivity, and find that a single linear operator is not sufficient to represent the local dynamics of these systems, but that on the contrary many operators are required. They present methods for characterizing the eigenvalues of all these operators and bounding them. In their own words, they “show that for topologically strongly connected networks asymptotic stability of the synchronized state can be demonstrated by graph-theoretical considerations.” They prove that for inhibitory interactions the synchronized state is stable, independently of the parameters and the network connectivity.