Trust levels in social networks

Dunbar's number is the cognitive limit of an individual to maintain stable relationships with others in his network. It is based on the size of the neocortex of the human brain. On the other hand, trust is one of the major issues for one while selecting members for his social network and the evolution of his social network with time. Trust and Dunbar's number are interconnected in the case of one's stable social network. Trust needs time to be built after several social interactions, intimacy, etc. In this paper, we try to provide answers to the following important questions related to social networks: (i) Do trust levels remain the same for individuals from one's perspective in his social network when the network size increases? (ii) What is the relation between the power-law exponent alpha and the trust cutoff? (iii) Do trust levels help to diffuse information quickly or vice versa to reach Dunbar's number 150 along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes? We find that there is a requirement for trust levels to increase among the same individuals in one's social network if the size of the network increases. As a relation between the power-law exponent alpha and the trust cutoff, it is found that alpha proportional to 1/(trust cutoff). Moreover, we also find that trust levels never help to diffuse information quickly or vice versa to reach Dunbar's number 150, along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes.