Group Intimacy and Network Formation

TLDR: A growing network model in which the strength of the intimacy among members is a tunable control parameter is proposed and it is found that it takes longer time for new nodes to make strong connections when the intimacy becomes stronger.

Abstract: Recent development of information technology allows us to efficiently communicate with others, sharing common interest and finding new friends. Numerous online communities are formed and disappear, but only a few survive the competition. Even after the survival, they eventually suffer from a decline as time goes on. Formation of a small intimate group within a community is often observed, and the members of this tightly-connected group play an important role providing strong activity in the community. However, the development of such an intimate group can exhibit a dark side effect: Other members in the community may feel left out and isolated, and newcomers may have hard time to join the already established intimacy. We believe that such a development of the tightly connected group of small number of intimate members can harm the further growth of the whole community, eventually reducing the community size. In this paper, we propose a growing network model in which the strength of the intimacy among members is a tunable control parameter. We observe how the size of the giant component is affected by the strength of the intimacy and find that it takes longer time for new nodes to make strong connections when the intimacy becomes stronger. Such alienated newcomers lose their connections and are driven out of the system, reducing the size of the connected component of the network.