We propose the Interferometric Graph Transform(IGT), which is a new class of deep unsupervised graph convolutional neural network for building invariant graph representations. Our first contribution is to propose a generic, complex-valued spectral graph architecture obtained from a generalization of the Euclidean Fourier transform. We show that our learned representation consists in both discriminative and invariant features, thanks to a novel greedy concave objective. From our experiments, we conclude that our learning procedure exploits the topology of the spectral domain, which is normally a flaw of spectral methods, and in particular our method can recover an analytic operator for vision tasks. We test our algorithm on various and challenging tasks such as image classification (MNIST, CIFAR-10), community detection (Authorship, Facebook graph) and action recognition from 3D skeletons videos (SBU,NTU), exhibiting a new state-of-the-art in spectral graph unsupervised settings.