We proposed a series of new radiomic features for PET image analysis base on graph theory and network analysis. Current PET radiomic features are mostly developed or transferred from CT images analysis which mainly focus on texture information. PET images usually contain functional information with lower resolution. Thus current radiomic features lack interpretability and specificity for PET image quantification. Meanwhile, a large number of texture features have similar definitions which cause severe redundancy for analysis and classification task. We proposed novel radiomic features based on graph theory that can specifically represent PET image characters. Using a set of tools in graph analysis, a new series of PET radiomic features that reveal different attributes of tumor, particularly intratumoral heterogeneity, are extracted. We applied our proposed method to lung cancer diagnosis and prognosis to evaluate performance of new features. Using ANN as classifier, our graph-based features outperformed traditional PET radiomic features. Furthermore, the combination of our features and tradition features can achieve an even better performance. It indicates that our graph-based features reveal significant and unique information of tumor in PET images.