Kriging models have been widely used in computer experiments for the analysis of time-consuming computer codes. Based on kernels, they are flexible and can be tuned to many situations. In this paper, we construct kernels that reproduce the computer code complexity by mimicking its interaction structure. While the standard tensor-product kernel implicitly assumes that all interactions are active, the new kernels are suited for a general interaction structure, and will take advantage of the absence of interaction between some inputs. The methodology is twofold. First, the interaction structure is estimated from the data, using a first initial standard Kriging model, and represented by a so-called FANOVA graph. New FANOVA-based sensitivity indices are introduced to detect active interactions. Then this graph is used to derive the form of the kernel, and the corresponding Kriging model is estimated by maximum likelihood. The performance of the overall procedure is illustrated by several 3-dimensional and 6-dimensional simulated and real examples. A substantial improvement is observed when the computer code has a relatively high level of complexity.