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In addition to Vanicek's original approach to network robustness, Tao's approach is introduced. Two sets of three deformation measures at each point of the network are then created due to the two approaches. To differentiate one approach from the other, three statistical tests are proposed: (1). Displacement tests examine the network as a whole: to what extent are the displacement vectors due to the two approaches different? These are referred to as global tests of the network's robustness between approaches. (2). Deformation tests, on the other hand, investigate to what extent the deformation vectors at individual points are different. These are referred to as local tests of the network's robustness between approaches. (3). Equivalence tests examine the network as a whole for the statistical equalities between the corresponding deformation measures generated by the two approaches. Furthermore, the spatial distribution of the influential observables, the observations which cause the largest deformations at individual points, between approaches is discussed