Framing biological networks like this is reminiscent of the persistent homology frameworks used to characterise proteins, 2D atomic glasses and zeolite structures (see refs. ; Ormrod ; ). Persistent homology approaches work by analysing objects called homology groups, generally constructed by placing a sphere of size r on each data point in a point cloud and expanding the size of r. When two spheres overlap, an edge is drawn between them and the simplices (polygons, polyhedra, or hyper-polyhedra) that are formed are analysed. The homology groups generated that way are often unwieldy ), and are most often simplified into a few useful outputs (among others): Betti numbers β n which measure the number of n-dimensional features; persistence diagrams which show how features appear and disappear as functions of r; and birth-death diagrams which show clusters of features appearing or disappearing. We can map the persistent homology framework onto the established network theory simply, as the first three Betti numbers correspond to the number of zero-, one-and two-dimensional features in the networks. In most persistent homology approaches, a persistence diagram charts at which value of a length scale (called a filtration parameter) various features first start to exist ('are born', in the language of persistent homology) or stop existing ('die') ). Persistence diagrams have been criticised (see, for example, refs. and Ormrod ) as they may be hard to interpret quantitatively, and they often reflect properties of a network that are difficult to visualise.