In this paper, we propose granularity as a new index to characterize the non-specificity of a summative kernel. This index is intended to reflect the behavior of a kernel in the usual signal processing applications. We show, in different experiments, that two kernels having the same granularity have very similar behavior. This granularity-based adaptation is compared to other adaptation methods. These experiments highlight the ability of the granularity index to measure the spreading and collecting properties of a summative kernel.