We discuss issues raised by applying von Neumann kernels to graphs with multiple communities. Depending on the parameter setting, Kandola et al.’s von Neumann kernels can identify not only nodes related to a given node but also the most important nodes in a graph. However, when von Neumann kernels are biased towards importance, top-ranked nodes are the important nodes in the dominant community of the graph irrespective of the communities where the target node belongs. To solve this “topic-drift” problem, we apply von Neumann kernels to the weighted graphs (community graph), which are derived from a generative model of links.