Multiple kernel learning (MKL), as a principled classification method, selects and combines base kernels to increase the categorization accuracy of Support Vector Machines (SVMs). The group method of data handling neural network (GMDH-NN) has been applied in many fields of optimization, data mining, and pattern recognition. It can automatically seek interrelatedness in data, select an optimal structure for the model or network, and enhance the accuracy of existing algorithms. We can utilize the advantages of the GMDH-NN to build a multiple graph kernel learning (MGKL) method and enhance the categorization performance of graph kernel SVMs. In this paper, we first define a unitized symmetric regularity criterion (USRC) to improve the symmetric regularity criterion of GMDH-NN. Second, a novel structure for the initial model of the GMDH-NN is defined, which uses the posterior probability output of graph kernel SVMs. We then use a hybrid graph kernel in the H-space for MGKL in combination with the GMDH-NN. This way, we can obtain a pool of optimal graph kernels with different kernel parameters. Our experiments on standard graph datasets show that this new MGKL method is highly effective.