In the last decade, usage of personal smartphones has tremendously increased. Almost everyone is using cell phones, which are communicating with location-aware devices. A large amount of trajectory data is produced from these devices and can be used for information services. One of the key elements in the mining of GPS or mobility data is the stay point recognition. A stay point is described as a location where a person frequently visits or stay for a long time period. In this work, we first introduce an algorithm to define a stay point for a person whose trajectory data is recorded with a smartphone. Later, with another algorithm, we define a graph model representing a person’s moving characteristics, which is built upon our stay point’s algorithm.