  A single human can be involved in a limited number of social relationships,
and the distribution of strengths of such relationships shows significant skew.
This skewness suggests that the costs and benefits of the social interactions
required to bond with others (social grooming) depend on the social
relationship strength: if they involved uniform costs and benefits, the
distribution would not be skew. Here, we show that the cost of social grooming
increases with the social relationship strength, and its gradient determines
the structures of these relationships in society as evident from an analysis of
data from six communication systems. This may be due to an increase in
communication volumes, such as number of characters and duration of calls,
along with an increase in the social relationship strength. We tested this
hypothesis using an individual-based simulation where social grooming costs
were assumed to increase linearly with the social relationship strength; this
is the simplest assumption. The results indicated that this model fitted all
data sets, i.e., it showed an explanation capacity for the phenomenon.
Additionally, an analysis of this simulation suggested that the gradient of
social grooming costs increases the width and shallowness of social
relationships in its communication system.
