We consider climate as a network of many dynamical systems and apply ideas from graph theory to a global data set to study its collective behavior. We find that the network has properties of ‘small-world’ networks (Nature 393 (1999) 440). A detailed investigation of the coupling architecture of this network reveals that the overall dynamics emerge from the interaction of two interweaved subnetworks. One subnetwork operates in the tropics and the other at higher latitudes with the equatorial one acting as an agent that establishes links between the two hemispheres. Both subsystems are ‘small-world’ networks, but there are distinct differences between the two subsystems. The tropical one is an almost fully connected network, whereas the mid-latitude one is more like a scale-free network characterized by dominant super nodes, and multifractal properties. This unique architecture may lead to new insights not only about the dynamics of the climate system but of other spatially extended complex systems with a large number of degrees of freedom.