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Computing (ktext {-}core)s is a fundamental and important graph problem, which can be applied in many areas, such as community detection, network visualization, and network topology analysis. Due to the complex relationship between different entities, dual graph widely exists in the applications. A dual graph contains a physical graph and a conceptual graph, both of which have the same vertex set. Given that there exist no previous studies on the (ktext {-}core) in dual graphs, we formulate a k-connected core ((ktext {-}CCO)) model in dual graphs. A (ktext {-}CCO) is a (ktext {-}core) in the conceptual graph, and also connected in the physical graph. Given a dual graph and an integer k, we propose a polynomial time algorithm for computing all (ktext {-}CCO)s. We also propose three algorithms for computing all maximum-connected cores ((MCCO)), which are the existing (ktext {-}CCO)s such that a ((k+1))-(CCO) does not exist. We further study a subgraph search problem, which is computing a (ktext {-}CCO) that contains a set of query vertices. We propose an index-based approach to efficiently answer the query for any given parameter k. We conduct extensive experiments on six real-world datasets and four synthetic datasets. The experimental results demonstrate the effectiveness and efficiency of our proposed algorithms.

K-Connected Cores Computation in Large Dual Networks