all the periodic orbits of upstream driving nodes of L-RCs have similar characteristic which is considerably di ff erent from normal nodes (see Fig. 5(c) for an example). Jointly using this particular feature and the above three general conclusions we can explore the missing L-RC drivings of source loop and all other missing L-RCs of source nodes with extremely high probability. For instance, in 10 random samples we successfully predict all the missing L-RCs of source nodes and recover the original main TFL structure without any error, of which the patching from Fig. 5(b) is shown in Fig. 5(d). Furthermore, we have tested many other cases with di ff erent system sizes, di ff erent numbers of existing L-RCs and di ff erent unknown L-RCs. We found that the above method of exploring unknown L-RCs works fairly well, and we can correctly reveal TFL loops with high probability. However, the method is not always successful. It may fail when di ff erent source nodes are linked by L-RCs having similar time series. The recover operations will be even more di ffi cult when both node data and interaction structure are incomplete. We will go further into these cases in our future study. In conclusion we have studied periodic self-sustained oscillations of target waves in excitable small-world networks. Based on interaction structures and oscillation data, a novel method of dominant phase-advanced driving (DPAD) path is proposed to study self-sustained oscillations in complex networks of nonoscillatory nodes and tree from loop (TFL) patterns can be drawn for oscillatory states. For oscillatory excitable small- world networks these TFL patterns show clearly 1D loops serving as oscillation sources and illustrate how waves propagate from the source loops to the whole tissues via various local and long-range couplings of small-world networks. More interestingly, with the instructive information of TFL patterns we can control and regulate oscillatory patterns of small-world networks with extremely high e ffi ciency. Self-sustainedly oscillatory complex networks of excitable cells exist significantly in wide fields, such as neural systems. Both the DPAD method and TFL structures are thus expected to be of broad interest in crossing fields of nonlinear dynamics, complex networks and their practical applications. In the present paper we consider only periodic oscillations of fixed complex networks. The ex tensions to nonperiodic oscillations (e.g., chaotic) and to the cases of noise and parameter-variation-driven oscillations, which occur popularly in practical situations, are future interesting tasks. VI. CONCLUSION 9