Topological Analysis Of SNS Social Networks

Nowadays an internet-based community called Social Network Services (SNS) society is becoming more and more popular all over the world. The idea of SNS comes from the research "Six Degrees of Separation phenomenon" initiated by Prof. Stanly Milgram. Our interests in SNS focus on its complex network properties since we find some common phenomenon in SNS shared by most of the complex networks, such as small-world effect and scale-free effect. In this paper we created two different SNS models and analyze these important properties of them by mathematical methods.The first model selected the famous SNS community Kaixin001 as our research object and we proposed this model to analyze how Kaixin001 expands with time. It is a hierarchy network containing many random links. We analyzed the three major properties of this model in its evolving process. The degree distribution follows the function p(k)=1/k+h and it's not a power-law distribution, which differs from many other complex network models developed before. We also get the result of a relatively high clustering coefficient and relatively low average path length which indicates the small world effect.The second model focused on the community property of an SNS. We mainly considered the connections among nodes and communities as well as the scale-free property and small world effect of this model. Via mean-field approach, we got the result of a power-law distribution p(k)∝k-γand a relatively high clustering coefficient. Then we used the result of the degree distribution to get the result of the average path length, which isl=ln(nlnnB/ln(nB)+1. These results illustrate that our model is both scale-free and a small world.