Brain regions are thought to be organized in large-scale networks, and studying interactions within and between such networks using functional magnetic resonance imaging (fMRI) could prove relevant for understanding brain's functional organization. Such interactions can be quantified by looking at their integration, a generalized measure of correlation. However, such a measure of integration cannot distinguish between mediated and direct interactions. In this paper, we introduce the concept of conditional integration, in order to provide an index of mediated interactions between networks. We first define conditional integration, and then apply it to both simulated and real fMRI datasets. In both cases results show that mediated interactions can be identified, demonstrating the contribution of conditional integration in functional connectivity studies.