The number of social relationships that a single human being can possibly be involved in is limited because individuals face time constraints (that is, time costs) in constructing and maintaining social relationships; furthermore, the distribution of the strength of such relationships (as measured by frequency of social interaction) looks significantly skewed (a power law distribution), that is, a few strong relationships and many weak relationships. This skewedness suggests that the costs and benefits of bonding with others depend on the strength of the social relationships: if it involves uniform costs and benefits, the distribution would not be skewed. The bonding is known as social grooming; that is, humans strategically construct their social relationships, and thus, complex human societies should also be strategically constructed. Therefore, it is important to know their strategies for understanding human societies. Previous studies provide evidence of social grooming strategies by examining the evolution and the difference between the various social grooming methods. However, quantitative laws that are important for theoretically understanding human societies are still open to investigation. Social big data is a particularly powerful tool for finding such laws. Therefore, we analyse data from six communication systems (Twitter, a social networking site providing two types of interactions, an avatar chat, a mobile phone and a short message service). We find a simple quantitative law by which social relationships are constrained Nm a (a41); here, N is the number of social relationships and m is a mean of the strength of those relationships. The fact that deep social relationships require higher costs per relationship than shallow relationships is suggested by a41 (if the both is equal then a will be 1), because the effect of m on the constraint increases with m. For exploring why a is greater than 1, we conduct an individual-based simulation where social grooming costs are assumed to increase linearly with the strength of social relationships. Our results indicate that this model fits all data sets; that is, it displays an explanation capacity for the phenomenon. In addition, an analysis of this simulation proves our assumption about the social grooming cost increasing with the strength of social relationships as being true. Moreover, it suggests that its gradient increases the width and shallowness of these relationships. The law and its causes suggest that mankind's evolution of social grooming has enabled changing social structures, and the phenomenon is because of the constraints of the social network generation. These findings will contribute towards an explanation of the evolution of the various social grooming methods of humans and their significantly large social group.