The experiment that Stanley Milgram conducted in the 1960s provided Essay

The experiment that Stanley Milgram conducted in the 1960s provided empirical evidence in favour of what is now referred to as t - Essay Example The results of the experiment have been proved by many other researchers in later studies, which explored the small-world effect in various types of networks. It has been verified that the small-world effect can be seen in different extent in a number of the real-world networks. The small-world phenomenon has made a great contribution in the theory of networks as it helped to better understand the structure and dynamics of the complex networks. This paper intends to discuss the Milgram's experiment and to explore in what extent the small-world effect can be found in three main classes of networks – random graphs, scale-free networks and small-world networks. Keywords: networks, social networks, small-world, six degree, random graph, scale-free networks. Introduction It is widely acknowledged that networks are all around people; and people themselves as socio-biological systems are, for the most part, products of biochemical reactions and social relationships occurring in netwo rks. Networks are studied since 1736, at first in the domain of mathematical graph theory (Biggs et al., 1986), which has been gradually developed into the solid branch of knowledge that studies nature and properties of different networks, from very simple to large and complex networks that have irregular structure and complex dynamics. Examples of such networks can be found everywhere in nature and in society – food networks of biological species, communication networks and the Internet, social networks between individuals, transportation networks, metabolic and neural networks, and many others. Nowadays the study of networks got significant achievements in understanding of specific features, some of which have been investigated in depth only in the past few decades, with the advent of information and communications technologies and, particularly, the Internet. One of the fundamental features of networks was discovered in 1967, when a famous social psychologist Stanley Milgr am conducted a series of experiments, revealing that in spite of the enormous number of the global population, our world is actually rather small - any individual on the planet can reach any other individual through about six contacts in their social network. The phenomenon was called the small-world effect, while the modern popular scientific literature often mentions it as the â€Å"six degrees of separation† effect (Watts, 1999). The results of the Milgram’s experiments have been proved in a large number of experiments of other researchers. The phenomenon appears to be extremely useful for understanding the structure and dynamics of processes that takes place in different networks, for example the dynamics of spread of information across the network, or the dynamics of diffusions of epidemic diseases in a society. The small-world effect can be viewed in different networks; however, each of these networks has the distinctive characteristics, related to its structure and dynamics, so there are certain differences in the manifestations of the small-world effect in various networks. This essay intends to discuss the Milgram's experiment and to explore in what extent the small-world effect can be found in networks, namely, in three main kinds of networks – in classical random graphs; in scale-free networks, introduced by Barabasi and Albert (1999); and in small-world networks, invented by Watts and Strogatz (1998). The paper is aimed to show