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Interdependent decisionmaking of individuals in social systems can be modelled by games played on complex networks. Players in such systems have bounded rationality, which influences the computation of equilibrium solutions. It has been shown that the ‘system rationality’, which indicates the overall rationality of a network of players, may play a key role in the emergence of scale-free or core-periphery topologies in real-world networks. In this work, we identify optimal topologies and mixing patterns of players which can maximise system rationality. Based on simulation results, we show that irrespective of the placement of nodes with higher rationality, it is the disassortative mixing of node rationality that helps to maximize system rationality in a population. In other words, the findings of this work indicate that the overall rationality of a population may improve when more players with non-similar individual rationality levels interact with each other. We identify particular topologies such as the core-periphery topology, which facilitates the optimisation of system rationality. The findings presented in this work may have useful interpretations and applications in socio-economic systems for maximizing the utility of interactions in a population of strategic players.

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.