  Our friends have more friends than we do. That is the basis of the friendship
paradox. In mathematical terms, the mean number of friends of friends is higher
than the mean number of friends. In the present study, we analyzed the
relationship between the mean degree of vertices (individuals), <k>, and the
mean number of friends of friends, <k_FF>, in scale-free networks with degrees
ranging from a minimum degree (k_min) to a maximum degree (k_max). We deduced
an expression for <k_FF> - <k> for scale-free networks following a power-law
distribution with a given scaling parameter (alpha). Based on this expression,
we can quantify how the degree distribution of a scale-free network affects the
mean number of friends of friends.
