Using integrate-and-fire networks, we study the relationship between the architectural connectivity of a network and its functional connectivity as characterized by the network's dynamical properties. We show that dynamics on a complex network can be controlled by the topology of the network, in particular, scale-free functional connectivity can arise from scale-free architectural connectivity, in which the architectural degree-correlation plays a crucial role.

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This work was partly supported by the National Science Foundation through grants DMS-0506287 and DMS-0636358.

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