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 ultra small-world organization, whereby
the graph’s diameter is independent of the network size over several
orders of magnitude, is still unknown.
I will 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.
Moreover, 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, 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.