Patterns and a generator of social networks: From the perspective of non-giant connected components

What patterns do non-giant connected components in a graph or network have? How do the non-giant connected components behave during their evolution over time? How can we model the time-evolving patterns of non-giant connected components? These questions are important for understanding the evolution of social networks, but they were seldom studied in previous work, which focused mainly on the giant connected component. In this paper, we study three real-world networks, and analyze some patterns of non-giant connected components. The main contributions of our work include the following aspects. First, we find that many non-giant connected components cannot stay in the networks for a long time. Most of them merge with one another or with the giant connected component. Second, we find that when those non-giant connected components die, the distribution of their node number follows a power law. Third, we design a graph generator to reproduce the observed patterns.