  We propose the notion of $k$-integration as a measure of equality of
opportunity in social networks. A social network is $k$-integrated if there is
a path of length at most $k$ between any two individuals, thus guaranteeing
that everybody has the same network opportunities to find a job, a romantic
partner, or valuable information. We compute the minimum number of bridges
(i.e. edges between nodes belonging to different components) or central nodes
(those which are endpoints to a bridge) required to ensure $k$-integration. The
answer depends only linearly on the size of each component for $k=2$, and does
not depend on the size of each component for $k \geq 3$. Our findings provide a
simple and intuitive way to compare the equality of opportunity of real-life
social networks.
