Graph-based representations have been proved powerful in computer vision. The challenge that arises with large amounts of graph data is that of computationally burdensome edit distance computation. Graph kernels can be used to formulate efficient algorithms to deal with high dimensional data, and have been proved an elegant way to overcome this computational bottleneck. In this paper, we investigate whether the Jensen-Shannon divergence can be used as a means of establishing a graph kernel. The Jensen-Shannon kernel is nonextensive information theoretic kernel, and is defined using the entropy and mutual information computed from probability distributions over the structures being compared. To establish a Jensen-Shannon graph kernel, we explore two different approaches. The first of these is based on the von Neumann entropy associated with a graph. The second approach uses the Shannon entropy associated with the probability state vector for a steady state random walk on a graph. We compare the two resulting graph kernels for the problem of graph clustering. We use kernel principle components analysis (kPCA) to embed graphs into a feature space. Experimental results reveal that the method gives good classification results on graphs extracted both from an object recognition database and from an application in bioinformation.