  We study a model for a statistical network formed by interactions between its
nodes and links. Each node can be in one of two states (Ising spin up or down)
and the node-link interaction facilitates linking between the like nodes. For
high temperatures the influence of the nodes on the links can be neglected, and
we get the Ising ferromagnet on the random (Erdos-Renyi) graph. For low
temperatures the nodes get spontaneously ordered. Due to this, the connectivity
of the network enhances and links having a common node are correlated. The
emerged network is clustered. The node-link interaction shifts the percolation
threshold of the random graph to much smaller values, and the very percolation
transition can become of the first order: the giant cluster coexist with the
unconnected phase leading to bistability and hysteresis. The model can be
applied to the striction phenomena in magnets and to studying opinion formation
in the sociophysical context.
