The decreasing cost of sequencing is leading to a growing repertoire of personal genomes. However, we are lagging behind in understanding the functional consequences of the millions of variants obtained from sequencing. Global system-wide effects of variants in coding genes are particularly poorly understood. It is known that while variants in some genes can lead to diseases, complete disruption of other genes, called loss-of-function tolerant, is possible with no obvious effect. Here, we build a systems-based classifier to quantitatively estimate the global perturbation caused by deleterious mutations in each gene. We first survey the degree to which gene centrality in various individual networks and a unified Multinet correlates with the tolerance to loss-of-function mutations and evolutionary conservation. We find that functionally significant and highly conserved genes tend to be more central in physical protein-protein and regulatory networks. However, this is not the case for metabolic pathways, where the highly central genes have more duplicated copies and are more tolerant to loss-of-function mutations. Integration of three-dimensional protein structures reveals that the correlation with centrality in the protein-protein interaction network is also seen in terms of the number of interaction interfaces used. Finally, combining all the network and evolutionary properties allows us to build a classifier distinguishing functionally essential and loss-of-function tolerant genes with higher accuracy (AUCxe2x80x8a=xe2x80x8a0.91) than any individual property. Application of the classifier to the whole genome shows its strong potential for interpretation of variants involved in mendelian diseases and in complex disorders probed by genome-wide association studies.