Why Are There Six Degrees of Separation in a Social Network?

A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultrasmall-world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the six degrees of separation is the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

Automated summary

A wealth of evidence shows that real-world networks have the small-world property and most social networks exhibit the six degrees of separation, where individuals are within six connections of each other. However, the reason behind the ultrasmall-world organization of social networks is still unknown. This study demonstrates that the six degrees of separation is a feature of equilibrium state in networks, where individuals balance their aspiration for centrality and the costs of forming and maintaining connections.