Archaea and particularly hyperthermophilic crenarchaea are hosts to many unusual viruses with diverse virion shapes and distinct gene compositions. As is typical of viruses in general, there are no universal genes in the archaeal virosphere. Therefore, to obtain a comprehensive picture of the evolutionary relationships between viruses, network analysis methods are more productive than traditional phylogenetic approaches. Here we present a comprehensive comparative analysis of genomes and proteomes from all currently known taxonomically classified and unclassified, cultivated and uncultivated archaeal viruses. We constructed a bipartite network of archaeal viruses that includes two classes of nodes, the genomes and gene families that connect them. Dissection of this network using formal community detection methods reveals strong modularity, with 10 distinct modules and 3 putative supermodules. However, compared to similar previously analyzed networks of eukaryotic and bacterial viruses, the archaeal virus network is sparsely connected. With the exception of the tailed viruses related to bacteriophages of the order Caudovirales and the families Turriviridae and Sphaerolipoviridae that are linked to a distinct supermodule of eukaryotic and bacterial viruses, there are few connector genes shared by different archaeal virus modules. In contrast, most of these modules include, in addition to viruses, capsidless mobile elements, emphasizing tight evolutionary connections between the two types of entities in archaea. The relative contributions of distinct evolutionary origins, in particular from nonviral elements, and insufficient sampling to the sparsity of the archaeal virus network remain to be determined by further exploration of the archaeal virosphere.