Certain capacity degradation levels increase travel times on road networks, while traffic demand remains met. Resilience of a road network is higher, if it can take-in higher levels of degradation without leaving any part of the demand unmet. It is important for planners to quantify this, and it can be obtained as the output of an optimization problem. The resultant measure of resilience is demand-specific. To generalize the resilience measure, its sensitivity to change in demand should be studied. We observe that irrespective of the difference in network size or network topology, resilience decreases with increase in demand. We perform computational experiments on different network topologies to investigate the relationship between network resilience and traffic demand. Based on this, we introduce the area under the demand-resilience curve as a generalized index of resilience (GIR). We compare the GIR with traditional network indicators and find that it is in certain ways, better. © 2016 World Scientific Publishing Company.