Duplications of genes encoding highly connected and essential proteins are selected against in several species but not in human, where duplicated genes encode highly connected proteins. To understand when and how gene duplicability changed in evolution, we compare gene and network properties in four species (Escherichia coli, yeast, fly, and human) that are representative of the increase in evolutionary complexity, defined as progressive growth in the number of genes, cells, and cell types. We find that the origin and conservation of a gene significantly correlates with the properties of the encoded protein in the protein-protein interaction network. All four species preserve a core of singleton and central hubs that originated early in evolution, are highly conserved, and accomplish basic biological functions. Another group of hubs appeared in metazoans and duplicated in vertebrates, mostly through vertebrate-specific whole genome duplication. Such recent and duplicated hubs are frequently targets of microRNAs and show tissue-selective expression, suggesting that these are alternative mechanisms to control their dosage. Our study shows how networks modified during evolution and contributes to explaining the occurrence of somatic genetic diseases, such as cancer, in terms of network perturbations.