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The social network of the Internet is interpreted as the consequences of invisible connection between humans. In the graph based studies the nodes are human beings and the edges represent various social relationships. SLN is a loosely coupled, self-organized semantic data model that link resources semantically. The interactions among users can be interpreted via SLN formation and evolution The interactive as well as intertwined behaviours are the foundation of network itself, at the same time, they shape the way how and where the network will evolve, enrich the semantics of the network and expand the network scale. This paper proposes a network growth model of SLN based on the semantics similarity and popularity of nodes. In our model, the nodes are Twitter blogs and are with semantics, the links are subscribing hyperlinks between blogs. The probability of link establishment between two nodes then calculated from the parameters given above. The data and experiments are based on Twitter blogs, which are the continuous results of interactions by users globally. We crawled the publicly accessible user interaction on blogs, obtaining a portion of the network's links between blogs and the hierarchy of each blog may exist in the whole scenarios. Results show that the statistic properties of SLN are in close analogy with that of social network. The studied network contains a number of high-degree nodes, these nodes are the cores which small groups strongly clustered, and low-degree nodes at the fringes of the network. However, some nodes with too much semantics (especially under one category) are in decreased chances of having links from newly added nodes. The reason may lies in that the over-abundant semantics remains confusion for knowledge acquiring.