This study establishes a simple Causal Map in order to understand the structure of Social Network Services(SNS). From this, the paper proposes a simulation with drawing Simulation Model and it examines whether a Dunbar Number is available for the emergence of collective intelligence based on an on-line network. Through my analytical research, it turn out both Closed SNS and Open SNS have their own Dunbar Number. However, it appear that Open SNS can expand infinitely as it has a unique property namely weak tie. This implies that it is significant for a system or policy to be developed in order to overcome the problem of Dunbar Number, whereas restricting the extension of a network by considering the Dunbar Number would have a negative impact on emergence of collective intelligence.