Understanding the impact of lifeline network failure during natural hazard events is key for disaster planning and mitigation. Lifeline networks – such as transportation, communication, power, water and sewage – are the critical infrastructure and essential services heavily relied upon for day-to-day living, the movement of goods, and, in a disaster, response and recovery. Lifelines comprise a large number of interconnected components, often spanning extensive geographic areas. There are also interdependencies between lifelines that can cause network failure to propagate in unforeseen ways. In September 2016, Southern Australian was hit by a severe storm that knocked over 22 transmission poles and damaged a number of generation facilities. This resulted in a state-wide power outage, leaving 1.67 million South Australian residents without electricity for nearly 12 hours, disrupting businesses and affecting other lifelines operation such as communications and traffic signals. Here we explore graph theory as a means of studying lifeline disruption using the Tokyo Subway network and a hypothetical hazard scenario.