Physical topologies are evolving from elementary survivable rings into complex mesh networks. Nevertheless, no topology model is known to provide an economic, systematic, and flexible interconnection paradigm for ensuring that those meshes bear resilience features. This paper argues that intrinsic resilience can be brought by twin graph topologies, as they satisfy equal length disjoint path property with minimal number of physical links. An exhaustive investigation is performed across twin graph families composing networks from 4 to 17 nodes, whereas diverse real-world topologies and ring networks are used as benchmarks. First, we illustrate the growing process, and discuss the topology diversity of twin graphs. We analyze the impact of single cable cuts between neighbouring nodes, then we stress topologies with 2, 3, and 4 simultaneous cable cuts. Improved resiliency is seen for neighbor nodes and also reduction of cut sets able to disconnect the twin topologies in comparison with real-world networks. Finally, we present as a use case the redesign of CESNET into a resilient network.