Institutions are the equilibrium states of games, and the emergence of institutions is an evolutionary, stochastic, and (social) structural dependence process of interactions among agents. In this paper, we address the relationship between the institutional emergence and the structure of social interactions under the context of (network) coordination games. The model here shows when the agents are socially restricted, and individual decision-making is based on mutual agreements, inefficient institutions will be the stable states in the long run, say, institutions are locked-in inefficiently. When the agents are not restricted socially, the institutional stability will wander between two states. The efficient institutions can emerge only as the agents are facing strong cost constraints and, are in the contexts with relative high certainties, for instance, as the interactive population size is becoming smaller.