Few-Shot Class-Incremental Learning (FSCIL) has gained considerable attention in recent years for its pivotal role in addressing continuously arriving classes. However, it encounters additional challenges. The scarcity of samples in new sessions intensifies overfitting, causing incompatibility between the output features of new and old classes, thereby escalating catastrophic forgetting. A prevalent strategy involves mitigating catastrophic forgetting through the Explicit Memory (EM), which comprise of class prototypes. However, current EM-based methods retrieves memory globally by performing Vector-to-Vector (V2V) interaction between features corresponding to the input and prototypes stored in EM, neglecting the geometric structure of local features. This hinders the accurate modeling of their positional relationships. To incorporate information of local geometric structure, we extend the V2V interaction to Graph-to-Graph (G2G) interaction. For enhancing local structures for better G2G alignment and the prevention of local feature collapse, we propose the Local Graph Preservation (LGP) mechanism. Additionally, to address sample scarcity in classes from new sessions, the Contrast-Augmented G2G (CAG2G) is introduced to promote the aggregation of same class features thus helps few-shot learning. Extensive comparisons on CIFAR100, CUB200, and the challenging ImageNet-R dataset demonstrate the superiority of our method over existing methods.