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As the backbone of many real-world complex systems, networks interact with others in nontrivial ways from time to time. It is a challenging problem to detect subgraphs that have dependencies on each other across multiple networks. Instead of devising a method for a specific scenario, we propose a generic framework to discover subgraphs in multiple interdependent networks, which generalizes the classical subgraph detection problem in a single network and can be applied to more practical applications. Specifically, we propose the Graph Block-structured Gradient Hard Thresholding Pursuit (GB-GHTP) framework to optimize interdependent networks with block-structured constraints, which enjoys 1) a theoretical guarantee and 2) a nearly linear time complexity on the network size. It is demonstrated how our framework can be applied to three practical applications: 1) evolving anomalous subgraph detection in dynamic networks, 2) anomalous subgraph detection in networks of networks, and 3) connected dense subgraph detection in dual networks. We evaluate our framework on large-scale datasets with comprehensive experiments, which validate our framework's effectiveness and efficiency.INDEX TERMS subgraph detection, sparse optimization, interdependent networks.

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