Correlation effects in a simple small-world network

We analyze correlation effects in a simple model of small world networks, first introduced in \cite{dm}, which is a ring of $N$ sites connected randomly to a distinguished site at the center. Any two sites connected in this way are interpreted to be connected by a shortcut. We enter correlations into this model by taking these random connections from an Ising distribution on the ring. We will show that correlations tend to decrease the small world effect.