Acharjee Santanu, Panicker Akhil Thomas
Department of Mathematics, Gauhati University, Assam, India.
Department of Physics, Cochin University of Science and Technology, Kerala, India.
Heliyon. 2023 Sep 15;9(9):e19850. doi: 10.1016/j.heliyon.2023.e19850. eCollection 2023 Sep.
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 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.
邓巴数是个体在其社交网络中与他人维持稳定关系的认知极限。它基于人类大脑新皮层的大小。另一方面，信任是一个人在选择社交网络成员以及社交网络随时间演变时的主要问题之一。在一个人的稳定社交网络中，信任和邓巴数是相互关联的。信任需要经过几次社交互动、亲密接触等之后的时间来建立。在本文中，我们试图回答以下与社交网络相关的重要问题：（i）当社交网络规模增加时，从一个人的角度来看，其社交网络中个体的信任水平是否保持不变？（ii）幂律指数α与信任阈值之间的关系是什么？（iii）信任水平是否有助于信息快速传播，反之亦然，在不同规模的网络中，随着5人、15人以及50人的层级结构达到邓巴数150？我们发现，如果社交网络规模增加，其社交网络中相同个体之间的信任水平需要提高。作为幂律指数α与信任阈值之间的关系，发现其为1/（信任阈值）。此外，我们还发现，信任水平永远不会有助于信息快速传播，反之亦然，在不同规模的网络中，随着5人、15人以及50人的层级结构达到邓巴数150。
