Ten years ago, Rivera and Lake decided to emphasize the series if genome fusions that seem to have been involved in the origin of the major phylogenetic groups by calling it the ring of Life rather than the Tree of Life:
Maria C. Rivera and James A. Lake. 2004. The Ring of Life provides evidence for a genome fusion origin of eukaryotes. Nature 431: 182-185).
This terminology has been repeated in a number of subsequent papers, including:
James McInerney, Davide Pisani and Mary J. O'Connell (2015) The Ring of Life hypothesis for eukaryote origins is supported by multiple kinds of data. Philosophical Transactions of the Royal Society of London B 370: 20140323.However, life is not that simple, and it has more recently become accepted that a set of inter-connected rings is involved in the metaphor, rather than the simple ring originally presented. Thus we now have the plural Rings of Life, instead.
James A. Lake and Janet S. Sinsheimer (2013) The deep roots of the Rings of Life. Genome Biology and Evolution 5: 2440-2448.
James A. Lake, Joseph Larsen, Brooke Sarna, Rafael R. de la Haba, Yiyi Pu, HyunMin Koo, Jun Zhao and Janet S. Sinsheimer (2016) Rings reconcile genotypic and phenotypic evolution within the Proteobacteria. Genome Biology and Evolution (in press).I think that the rest of us would still call each of these diagrams a network. Indeed, most of the metaphors that have been used over the years can also be called a network (see Metaphors for evolutionary relationships).