Over the past decades, supply chains have grown longer and became interconnected as a result of globalisation and rising cost pressures (Christopher and Holweg, 2011). Interconnectedness implies that a failure in one supply chain entity can potentially cascade across the whole network (Schmitt and Singh, 2012), making risk monitoring and mitigation challenging. Suppliers of multiple tiers are tied together creating emergent, yet predictable connection patterns, described as “supply network topology” (Thadakamalla et al., 2004). Studies on network topology, conducted under the framework of network science aim to unveil the behavioural phenomena of interconnected systems, which cannot be well understood from the perspective of a single entity. Understanding how the decision-making of multiple interconnected entities influence overall network resilience is necessary to cope with disruptions effectively because failures are more likely to propagate in certain topologies (Watts, 2002). Supply Chain Risk Management (SCRM) methods rarely consider the impact of disruptions on the extended supply network, where the term extended refers to ties beyond a firm’s direct suppliers and customers. The relationship between supply network topology and the effectiveness of recovery from disruptions using risk management strategies has not yet been explored. We aim to address this gap as follows. After reviewing previous work done in the field of SCRM and complex supply networks, we employ a modelling approach, where several theoretical network topologies based on the extant empirical literature are generated. The generated topologies are used to configure a supply network, after which the networks are subjected to random disruptions. Two SCRM strategies, namely inventory mitigation and contingent rerouting, are applied and the extent to which these strategies are able to enhance network recovery is observed. Our results sound a cautionary note. We find that the effectiveness of the two SCRM strategies is moderated by the topology of the supply network and that an increased understanding of supply network topology is necessary to underpin the choice of an effective strategy. First, it is shown that inventory mitigation outperforms contingent rerouting in a complex supply network setting regardless of topology. A key lesson is that random topologies need significantly higher inventory levels to recover from disruptions than scale-free networks. It is also observed that contingent rerouting is not effective for scale-free networks due to low numbers of alternative suppliers, particularly for short-term disruptions. We then explore targeted risk management, where only suppliers which suffered the most from disruptions apply a risk management strategy. Targeting suppliers does not always result in cost reduction. On the contrary, targeted inventory mitigation might significantly increase costs when the network is exposed to rare disruptions due to excessive inventory being kept for long periods of time. Targeted contingent rerouting creates inventory oscillations when network is exposed to short-lasting disruptions, resulting in decreased fill-rates and increased costs. Our work motivates further studies on the relationship between the functionality and performance of supply networks and their topology.