Post-event impact assessments (PEIAs) are essential to elucidate disasters' drivers and better anticipate future events. The 2021 Tajogaite eruption of Cumbre Vieja (La Palma, Spain) demonstrated the various orders of impact due to compound volcanic products (i.e., lava, tephra, gas) affecting a highly interconnected and low redundant infrastructure, typical of insular environments. Using a forensic approach, we discretise the causal order of cascading impacts, from physical damage (first order) to loss of functionality of the road network (second order) and subsequent systemic disruption of emergency management and socio-economic sectors (third order). Based on graph theory, we apply a comprehensive network analysis to quantify the loss of functionality and resulting effects, based on the spatiotemporal evolution of centrality indicators. The consequences on dependent systems are expressed in terms of increased driving time syn- and post-eruption between target locations for emergency (evacuation), public health (hospital), agriculture (crops-market), and education (schools). Graph indicators are objective measures of system performance during (disturbing/degraded states) and after the eruption (restorative state), when two new roads where rapidly built to reconnect the island. This study demonstrates how network analyses, informed by comprehensive PEIAs, can accurately capture complex systemic disturbances, thus highlighting its potential for risk assessments.