The functional connectome is organized into several separable intrinsic connectivity networks (ICNs) that are thought to be the building blocks of the mind. However, it is currently not well understood how these networks are engaged by emotionally salient information, and how such engagement fits into emotion theories. The current study assessed how ICNs respond during the processing of angry and fearful faces in a large sample (N = 843) and examined how connectivity changes relate to the ICNs. All ICNs were modulated by emotional faces and showed functional interactions, a finding which is in line with the "theory of constructed emotions" that assumes that basic emotion do not arise from separable ICNs but from their interplay. We further identified a set of brain regions whose connectivity changes during the tasks suggest a special role as "affective hubs" in the brain. While hubs were located in all ICNs, we observed high selectivity for the amygdala within the subcortical network, a finding which also fits into "primary emotion" theory. The topology of hubs corresponded closely to a set of brain regions that has been implicated in anxiety disorders, pointing towards a clinical relevance of the present findings. The present data are the most comprehensive mapping of connectome-wide changes in functionally connectivity evoked by an affective processing task thus far and support two competing views on how emotions are represented in the brain, suggesting that the connectome paradigm might help with unifying the two ideas.