Graph played an important role in defining the notion of the world map of Maiar Game. Besides the network applications, graphs and digraphs serve as natural models for a host of other applications and this motivation lead us use it to model the world map of the Maiar Game. The implementation of the graph or the digraph ADT of the Maiar world-map is described as an algorithm. The considered architecture includes asynchronous communication mechanisms, which are modeled in the Jxta-based Maiar API and achieved by message exchanges.