This paper proposes a quantitative approach for measuring the resilience of the network components and the network itself. This study introduces a conceptual framework featuring the ability of the network system to adopt alternative plans when a component is disrupted. As a first step toward measuring network resilience, the component resilience is defined and quantified as a function of criticality, disruption frequency, disruption impact, and recovery capability. This quantification approach reflects the effect of component level disruption on the network. Hence, it is proposed that the network resilience is measured by the resilience of network component having the lowest resilience index. Efforts to enhance network resilience often require financial resources. Therefore, an optimization model is further introduced to maximize the network resilience under budget constraint through reinforcing the weakest components in the network. The proposed approach can help decision-makers assess the network resilience status and compare with it other networks, identify and improve components with low resilience, evaluate the cost of resilience improvement, and determine the extent of enhancement that can be achieved under a given budget limitation. Numerical experiments are conducted to illustrate our methodology using a supply chain network and a power network. Both examples show that considering the ability of the network to use alternative plans can enhance network resilience and result in lower demand loss when a disruption occurs.