Fig. 1

Topology and geometry of disease modules. a A toy protein network embedded in \(\mathbb {H}^{2}\) and the gene products associated with a disease highlighted in red. The resulting DM is fragmented in 4 components and the largest one (LCC) has size 5. The topologically-closest protein to A is B (d _s =3) and its geometrically-closest protein is C (d _H =10.387), although it is 4 hops away from A. b The 157 studied DMs are split into several connected components in the hPIN. c The LCC size of each DM was compared with a random distribution of LCC sizes via a z-test. d The average of the shortest paths from each disease protein to its topologically-closest other DM member (〈d _s 〉) was compared with random expectation via a z-test. e The average of the hyperbolic distances from each disease protein to its geometrically-closest other DM member (〈d _H 〉) was compared with random expectation via a z-test. The red lines correspond to the significance level α=0.05 and the blue ones to the situation in which all proteins associated with a disease form a single connected component