Quantifying the robustness of complex networks with heterogeneous nodes

The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous in nature. In this work, we propose a robustness measure called fitness-incorporated average network efficiency, that attempts to capture the heterogeneity of nodes using the ‘fitness’ of nodes in measuring the robustness of a network. Further, we adopt the same measure to compare the robustness of networks with heterogeneous nodes under varying topologies, such as the scale-free topology or the Erdős–Rényi random topology. We apply the proposed robustness measure using a wireless sensor network simulator to show that it can be effectively used to measure the robustness of a network using a topological approach. We also apply the proposed robustness measure to two real-world networks; namely the CO₂ exchange network and an air traffic network. We conclude that with the proposed measure, not only the topological structure, but also the fitness function and the fitness distribution among nodes, should be considered in evaluating the robustness of a complex network.