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Dynamic communication and routing play important roles in the human brain in order to facilitate flexibility in task solving and thought processes. Here, we present a network perturbation methodology that allows investigating dynamic switching between different network pathways based on phase offsets between two external oscillatory drivers. We apply this method in a computational model of the human connectome with delay-coupled neural masses. To analyze dynamic switching of pathways, we define four new metrics that measure dynamic network response properties for pairs of stimulated nodes. Evaluating these metrics for all network pathways, we found a broad spectrum of pathways with distinct dynamic properties and switching behaviors. We show that network pathways can have characteristic timescales and thus specific preferences for the phase lag between the regions they connect. Specifically, we identified pairs of network nodes whose connecting paths can either be (1) insensitive to the phase relationship between the node pair, (2) turned on and off via changes in the phase relationship between the node pair, or (3) switched between via changes in the phase relationship between the node pair. Regarding the latter, we found that 33% of node pairs can switch their communication from one pathway to another depending on their phase offsets. This reveals a potential mechanistic role that phase offsets and coupling delays might play for the dynamic information routing via communication pathways in the brain.