## 1 Introduction  
With the development of economic globalization, the increasing vulnerability of supply networks (SN) has drawn substantial attention to risk management [1; 2]. Any event that negatively affects the information and material flow between suppliers and demanders should be considered as a risk to the disruption [3]. The resilience of a SN is a new concept related to its ability to mitigate vulnerability, which has been focused on in the last few years [4; 5]. Merriam-Webster defines resilience as \"the ability to recover or adjust easily to misfortune\" [6]. A resilient SN is able to cope with (or react to) unexpected disruptions and recover quickly to the planned predisaster state [7], which results in the evolution of new practices to construct resilient SNs. Network resilience can be defined in two fundamental dimensions: (i) vulnerability, or the lack of ability of a network to withstand disruptive events and maintain its maximum possible level of performance in the immediate aftermath of disruptions; and (ii) recoverability, or the ability of the network to return to a desired level of performance within a recovery time horizon [8]. These two dimensions describe components of robustness and rapidity in the resilience triangle. The resilience capacity of a system is defined as a function of three capacities: (i) absorptive capacity, or the extent to which a network is able to absorb shocks from disruptive events; (ii) adaptive capacity, or the extent to which a system can quickly adapt after a disruption by temporary means; and (iii) restorative capacity, or the extent to which the system can recover from a disruption or be reconstructed in the long-term [9]. Despite a growing number of research studies on SN resilience, there is still a lack of knowledge about resilient recovery. Moreover, few studies have attempted to measure and control resilient recovery [10]. Considering all the above factors, this research attempts to seek answers to the following questions:  
1. What is the most efficient method of resilient recovery of the SN? 2. How should the resilient recovery of the SN be measured? 3. How should the backbone of the network for resilient recovery be identified? 4. How should the resilient recovery of the SN be controlled? The idea of network synchronization is to design appropriate controllers so that the network state can be tracked and synchronized to the target state. The study of synchronization is no longer limited to nodes within a network (internal synchronization), but also extends to synchronization between networks (outer synchronization) [11]. Outer synchronization can help the corresponding nodes to achieve the identical state. It is widely established that resilience means a return to a scheduled state [12]. Therefore, resilient recovery is a process of outer synchronization between the actual network after the disruption and the scheduled network before the disruption. Therefore, outer synchronization provides a feasible method for resilient recovery. The effectiveness of resilient recovery measures is a key issue in engineering applications. However, most studies see the importance of network components as a standard for resilience measures [13], which is considered \"memoryless\", for the reason that this resilience standard does not take into account the previous information. It may have the same value of resilience with different restoration curves and different degrees of effectiveness. Therefore, resilience measures rely on the recovery time [6]. In this study, two indicators, namely recovery degree and recovery time, are introduced to quantify the effectiveness of resilient recovery. We propose a new method of outer synchronization-based recovery effectiveness measurement, which serves as the methodological background for the adoption of recovery measures.