# Preference for Number of Friends in Online Social Networks
## 1 Introduction  
Numbers play a prominent role in the daily life of human beings. Just as the motto of the Pythagorean school goes, all is number [1, 2, 3]. The Pythagoreans used numbers to describe the world, attempted to capture the essence of all existing things, and associated social meanings with the numbers. For example, they believed that odd numbers were masculine, even numbers were feminine [4], the number one stood for the origin of everything, and the number ten was the number of the universe [5]. This kind of mystical worship for numbers became Pythagorean numerology, which affected many aspects of people's life in turn. Up to the present, similar numerology or number preference still widely exists in various cultures around the world [6, 7, 8, 9]. For example, the number eight represents good fortune and wealth, while the number four represents bad fortune in China [10, 11, 12]. Similarly, in a few Christian countries, the number thirteen is seen as unlucky [13, 14]. However, in Italy, thirteen is considered a lucky number. In modern society, the preference for numbers has a profound influence on people's decision making, and it has been extensively studied in the field of consumer research [15, 16, 17, 18, 19, 20, 21, 22, 23, 24].  
With the rapid development of the Internet and the increasing popularity of intelligent terminals, global online social media represented by Facebook, Twitter, WeChat, Weibo,and TikTok have formed a new trans-national, trans-ethnic, and trans-cultural online community with more than billions of people [25; 26; 27; 28; 29]. These social media platforms play an indispensable role in daily life. A large amount of data on user interaction behavior provides a solid foundation for studying the online presentation of human behavior. Based on the data generated by social media, we can infer users' characteristics [30; 31] and design a more accurate recommendation system [32]. In addition, users' social profiles can reflect their personality [33; 34; 35] and their preferences for different ways of information consumption [36]. In terms of specific applications, the data of user interaction on social media can be applied for event prediction [37; 38], robot detection [39; 40], and fake news detection [41]. Further, social media also provides us a large-scale data of network topology and information transmission trajectory. Thus, we can analyze the evolution of users' attention [42] and discourse power in the network [43].  
In this present research, we focus on the preference for numbers in the online social network Sina Weibo, especially the choice for the number of friends. We find that the distribution of users' friend number has a very significant peak near 200. Weibo's network structure formation mechanism is the same as that of Twitter. Users are free to decide who and how many to follow (i.e., friends). However, they cannot determine who follows themselves (i.e., followers) and the corresponding number. In this system, the numbers of users' followers are usually heterogeneous [44; 45]. In other words, most users often have a quite limited number of followers, while a minority of users have a large number of followers, such as social celebrities and entertainment stars. However, due to the limited time and attention of the users, they can only maintain effective social relationships with a certain number of friends. Therefore, the numbers of effective friends of the users are generally homogeneous [46], such as Dunbar number (150) [47]. In this paper, we mainly study users in Sina Weibo who have a particular preference for 200 friends and investigate their important social properties, such as activity, popularity, attention tendency, portraits evolution, regional difference, economic, and educational development level.