Using graph theory to re-verify the small world theory in an online social network word

The development in social network services changes our traditional social structure. Nowadays, people can easily communicate with their old friends or even make new ones. The "Small World Theory" [5] states that the median path length equal to 6 when posting letters through intermediaries, but researchers have not prove this theory completely until now. Because of social networks our world becomes smaller and smaller. In this paper, we propose new ideas about the "Small World Theory". We performed our experiment on Facebook platform to collect social data. Additionally, the graph database is used to conduct further analyses. To re-verify the "Small World Theory" and to extend this theory, we focused on the degree of separation and control the size of the dataset. The experimental results show that our dataset is "Four Degrees of Separation", and this conclusion can be extended to the whole world by further experiments.