The impressive ability of large language models to generate natural text across various tasks has led to critical challenges in authorship authentication. Although numerous detection methods have been developed to differentiate between machine-generated texts (MGT) and human-generated texts (HGT), the explainability of these methods remains a significant gap. Traditional explainability techniques often fall short in capturing the complex word relationships that distinguish HGT from MGT. To address this limitation, we present LM$^2$otifs, a novel explainable framework for MGT detection. Inspired by probabilistic graphical models, we provide a theoretical rationale for the effectiveness. LM$^2$otifs utilizes eXplainable Graph Neural Networks to achieve both accurate detection and interpretability. The LM$^2$otifs pipeline operates in three key stages: first, it transforms text into graphs based on word co-occurrence to represent lexical dependencies; second, graph neural networks are used for prediction; and third, a post-hoc explainability method extracts interpretable motifs, offering multi-level explanations from individual words to sentence structures. Extensive experiments on multiple benchmark datasets demonstrate the comparable performance of LM$^2$otifs. The empirical evaluation of the extracted explainable motifs confirms their effectiveness in differentiating HGT and MGT. Furthermore, qualitative analysis reveals distinct and visible linguistic fingerprints characteristic of MGT.