Stability in social networks.

Dunbar's number is the cognitive limit of human beings to maintain stable relationships with other individuals in their social networks, and it is found to be 150. It is based on the neocortex size of humans. Usually, Dunbar's number and related phenomena are studied from the perspective of an individual. Dunbar's number also plays a crucial role in evolutionary psychology and allied areas. However, no study done so far has considered a couple who are in a stable relationship as a system from the perspective of Dunbar's number and its hierarchy layers. In this paper, we study the impact of Dunbar's number and Dunbar's hierarchy from the perspective of a couple by studying mathematically the conjoint Dunbar graphs for a couple. The cost of romance is the loss of almost two people from one's support network when a human being enters into a new relationship. Thus, we obtain mathematically that there is no significant change in one's friendship if human beings spend negligible time with their partners. Also, along with marriage and friendship development, we attempt to assess how a person's social network structure holds up over the course of a romantic relationship. The stability of personal social networks is discussed through soft set theory and balance theoretic approach.