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Abstract：
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 α 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 α and the trust cutoff, it is found that α∝ 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.
摘要：
邓巴的数字是个人在他的网络中与他人保持稳定关系的认知极限。它基于人脑新皮层的大小。另一方面,信任是一个人在为他的社交网络选择成员以及他的社交网络随时间的演变时的主要问题之一。信任和邓巴的号码在一个人的稳定的社会网络的情况下是相互关联的。信任需要时间在几次社交互动后建立，亲密,等。在本文中,我们试图提供与社交网络相关的以下重要问题的答案:(i)当网络规模增加时,从一个人的角度来看,个人的信任级别是否保持不变?(ii)幂律指数α和信任截止值之间有什么关系?作为幂律指数α与信任截止之间的关系，结果发现，α腙1/(信任截止)。此外，我们还发现，信任级别永远不会帮助快速传播信息，反之亦然，以达到Dunbar的150号，以及不同规模的网络中的5、15和50个人的层次结构。
