Training unsupervised speech recognition systems presents challenges due to GAN-associated instability, misalignment between speech and text, and significant memory demands. To tackle these challenges, we introduce a novel ASR system, ESPUM. This system harnesses the power of lower-order N-skipgrams (up to N=3) combined with positional unigram statistics gathered from a small batch of samples. Evaluated on the TIMIT benchmark, our model showcases competitive performance in ASR and phoneme segmentation tasks. Access our publicly available code at https://github.com/lwang114/GraphUnsupASR.