Individual-specific networks, defined as networks of nodes and connecting edges that are specific to an individual, are promising tools for precision medicine. When such networks are biological, interpretation of functional modules at an individual level becomes possible. An under-investigated problem is relevance or ”significance” assessment of each individual-specific network. This paper proposes novel edge and module significance assessment procedures for weighted and unweighted individual-specific networks. Specifically, we propose a modular Cook’s distance using a method that involves iterative modeling of one edge versus all the others within a module. Two procedures assessing changes between using all individuals and using all individuals but leaving one individual out (LOO) are proposed as well (LOO-ISN,MultiLOO-ISN), relying on empirically derived edges. We compare our proposals to competitors, including adaptions of OPTICS, kNN, and Spoutlier methods, by an extensive simulation study, templated on real-life scenarios for gene co-expression and microbial interaction networks. Results show the advantages of performing modular versus edge-wise significance assessments for individual-specific networks. Furthermore, modular Cook’s distance is among the top performers across all considered simulation settings. Finally, the identification of outlying individuals regarding their individual-specific networks, is meaningful for precision medicine purposes, as confirmed by network analysis of microbiome abundance profiles.