The protection of network infrastructure and services is one of the main issues network managers face today. This paper investigates this matter through the study of network resilience. A resilience factor (RF) is proposed to take into account topological aspects of the network and also the amount of traffic losses under stress conditions. The proposed factor is evaluated using a real network backbone (RNP). Results obtained showed that the resilience factor is consistent and can be employed to support network managers decisions about network expansions, link additions and removals. Such decisions improve network robustness making it less vulnerable to attacks and failures.