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Integrating coarse-grained reconfigurable architectures (CGRAs) into a System-on-a-Chip (SoC) presents many benefits as well as important challenges. One of the challenges is how to customize the architecture for the target applications efficiently and effectively without explicit design space exploration. In this paper we present a novel methodology for incremental interconnect customization of CGRAs that can suggest a new interconnection architecture that can maximize the performance for a given set of application kernels while minimizing the hardware cost. Applying the inexact graph matching analogy, we translate our problem into graph matching taking into account the cost of various graph edit operations, which we solve using the A* search algorithm with a heuristic tailored to our problem. Our experimental results demonstrate that our customization method can quickly find application-optimized interconnections that exhibit 70% higher performance on average compared to the base architecture, with relatively little hardware increase in interconnections and muxes.