Aiming at serving the interdisciplinary demand in network science, this paper introduces a new concept for complex networks, named network stiffness, which is extracted from structural engineering by assuming that a complex network behaves similarly with a structured framework. This analogy allows interpreting that a complex network can resist against any cause attempting to induce deformation changes to the network's structure, regardless of whether the network is material or not. Within this framework, this paper examines the context of applying the conceptual analogy of stiffness from the field of structural engineering to network science and then it develops computational approaches capturing different aspects of network stiffness so that to be used in complex network analysis. The implementation of these approaches to a real-world network (global inbound tourism network) shows that stiffness can produce interesting insights to complex network analysis about the factors related to changes caused to the structure and the status of a complex network.