Linking via social similarity: The emergence of community structure in scale-free network

We propose a simplified model which exhibits community structure, power-law degree distribution and high clustering. Every vertex is a social one with a social identity. The preferential attachment of Barabasi-Albert model is incorporated with social similarity. When a newly added vertex makes a new link, it first selects a certain group of vertices with a probability by considering the social distances between it and all existing vertices. This is the linking mechanism via social similarity, simply known as the attraction of homogeneity. Then, in the group, a new edge links the new one to another one using preferential attachment. Via this mechanism, community structure emerges in scale-free networks. Theoretical calculation and implementing a community-finding algorithm both show that the measure of generated community structure increases with the strength of linking via social similarity. Furthermore, we introduce ldquotriad formationrdquo into our model to reproduce a high clustering. Our model is elegant for modeling large-scale social networks with community structure and has potential applications in studying dynamics on networks with community structure.