Small-World Effect in Networks - Essay Example

The small-world effect can be seen to a different extent in a number of real-world networks. The small-world phenomenon has made a great contribution to the theory of networks as it helped to better understand the structure and dynamics of complex networks. This paper intends to discuss Milgram's experiment and to explore to 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 networks. 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 the 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 the 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 Milgram 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 “six degrees of separation” effect (Watts, 1999). The results of Milgram’s experiments have been proved in a large number of experiments by other researchers. The phenomenon appears to be extremely useful for understanding the structure and dynamics of processes that take place in different networks, for example, the dynamics of the spread of information across the network, or the dynamics of diffusions of epidemic diseases in society.

The small-world effect can be viewed in different networks; however, each of these networks has 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 Milgram's experiment and to explore to 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 that the small-world phenomenon, exhibited in most of the real-world networks, can be represented by all main today’s models of networks but to a different extent.