Orientation in social networks

Stanley Milgram’s small world experiment presents “six degrees of separation” of our world. One phenomenon of the experiment still puzzling us is that how individuals operating with the social network information with their characteristics can be very adept at finding the short chains. The previous works on this issue focus whether on the methods of navigation in a given network structure, or on the effects of additional information to the searching process. In this paper, we emphasize that the growth and shape of network architecture is tightly related to the individuals’ attributes. We introduce a method to reconstruct nodes’ intimacy degree based on local interaction. Then we provide an intimacy based approach for orientation in networks. We find that the basic reason of efficient search in social networks is that the degree of “intimacy” of each pair of nodes decays with the length of their shortest path exponentially. Meanwhile, the model can explain the hubs limitation which was observed in real-world experiment. China has a famous shortest poem titled life: net (by poet Bei Dao). This one word poem tells us that any one in the world is living in the invisible social networks. In the 1960s, Stanley Milgram has revealed a striking feature of these networks by his famous experiment [1]. He showed us that any two people can be linked by a short chain of friends. The average length of the chains is about six, which is quite remarkably close to Karinthys prediction 40 years earlier [2]. This fascinating result has been popularized in the 1990s by John Guare’s successful play “six degrees of separation” [3] and has been known as small world phenomena. More recent empirical studies using the Internet have demonstrate the similar conclusion [4, 5]. Actually, Milgram’s experiment showed us two issues of special interest: first, is the existence of short paths, and second, is the ability of people at finding them efficiently. The first issue has been extensively studied, especially with the Watts-Strogatz Small-World Network (SW) model (see Ref. [6, 7] and references therein for review, such as [8, 9]). Here we focus only on the second issue that we still lack an equally complete understanding. [email protected] [email protected]