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Robustness of network of networks (NON) has been studied only for dependency coupling (Gao et al., 2012) and only for connectivity coupling (Leicht and Souza, arxiv: 0907.0894). The case of network of networks with both interdependent and interconnected links is more complicated, and also more close to real-life coupled network systems. Understanding the robustness of NON with interdependent and interconnected links is helpful to design resilient infrastructures. Here we develop a framework to study analytically and numerically the robustness of this system with no-feedback and feedback conditions for the case of starlike NON. When assumed that all degree distributions of the connectivity intra-and inter-links are Poissonian, we find that the system undergoes from second order through hybrid order to first order phase transition as coupling strength q increases. Additionally, for both conditions, the results …