Data structure is the key in Edge Computing where various types of data are continuously generated by ubiquitous devices. Within all common data structures, graphs are used to express relationships and dependencies among human identities, objects, and locations; and they are expected to become one of the most important data infrastructure in the near future. Furthermore, as graph processing often requires random accesses to vast memory spaces, conventional memory hierarchies with caches cannot perform efficiently. To alleviate such memory access bottlenecks in graph processing, we present a solution through vertex accesses scheduling and edge array re-ordering, in parallel with the execution of graph processing application to improve both temporal and spatial locality of memory accesses, especially for edge-centric graphs which are popular means in handling dynamic graphs. Our proposed architecture is evaluated and tested through both trace-based cache simulations and cycle-Accurate FPGA-based prototyping. Evaluation results show that our proposal has a potential of significantly reducing the quantity of Miss-Per-Kilo-Instructions (MPKI) for Last Level Cache (LLC) by 56.27% on average.