Understanding the neural mechanisms of suicidal behavior is crucial. While regional brain alterations have previously been reported, knowledge about brain functional connectomics is currently limited. Here, we investigated differences in global topologic network properties and local network-based functional organization in both suicide attempters and suicide relatives. Two independent samples of depressed suicide attempters (N = 42), depressed patient controls (N = 43), healthy controls (N = 66) as well as one sample of healthy relatives of suicide victims (N = 16) and relatives of depressed patients (N = 16) were investigated with functional magnetic resonance imaging in the resting-state condition. Graph theory analyses were performed. Assortativity, clustering coefficients, global efficiency, and rich-club coefficients were calculated. A network-based statistic approach was finally used to examine functional connectivity matrices. In comparison to healthy controls, both patient groups showed significant reduction in assortativity, and decreased functional connectivity in largely central and posterior brain networks. Suicide attempters only differed from patient controls in terms of higher rich-club coefficients for the highest degree nodes. Compared to patient relatives and healthy controls, suicide relatives showed reduced assortativity, reduced clustering coefficients, increased global efficiency, and increased rich-club coefficients for the highest degree nodes. Suicide relatives also showed reduced functional connectivity in one anterior and one posterior sub-network in comparison to healthy controls, and in a largely anterior brain network in comparison to patient relatives. In conclusion, these results suggest that the vulnerability to suicidal behavior may be associated with heritable deficits in global brain functioning - characterized by weak resilience and poor segregation - and in functional organization with reduced connectivities affecting the ventral and dorsal prefrontal cortex, the anterior cingulate, thalamus, striatum, and possibly the insula, fusiform gyrus and the cerebellum.