Fig 3. Vascular graph clustering.

(a) Community clustering applied to the vascular network by using an unweighted vascular graph representation, w₀. Color codes for community membership. (b) and (c) Image volume rendering and the vascular graph segmentation, respectively, of a sub-volume (∼100μm width) extracted in a dense and modular area of the tissue near the central lymph node (white dotted rectangle depicted in (a)). (d) Schematic illustration of vascular communities; (e) structural community graph, with the number of vessels connecting two communities as edges weights (5 and 1 here); and (f) bi-functional community graph with in/out fluxes Q_ij as edges weights. (g) Graph clustering of the communities for geometrical based weight (w₂, curvilinear distance) and (h) perfusion based weight (hydraulic resistance w₃); the disks are located in community centers projected in the (x, y) plane with sizes coding for volumes and color for vascular density (volumic ratio from 0% to 20%) illustrated with a cold-to-warm color scale. (i) Linear regressions of the scatter plot of number of vessels between each pair of communities N_ev versus number of vessels in the community N_iv (for each community in (d), number of colored edges vs. number of black edges). Full lines are the linear regressions for each clustering weight w_i. w₀ no weight (slope s = 0.61); w₁ Euclidean distance (cf. Fig 2(a)) (s = 0.62); w₂ curvilinear distance (cf. Fig 2(a)) (s = 0.66); w₃ hydraulic resistance (Cf. S2 Text) (s = 0.25); w₄: hydraulic conductance (Cf. S2 Text) (s = 0.28). The gray curve is the result of Blinder et al. [5] with s = 0.83. Dashed lines delimit the boundaries of weak communities (therefore having strong connections between units) with slopes s = 2/3 and s = 1. Shaded areas are the standard errors associated with each regression. The linear regressions are normalized with zero offset at the origin. (j) Non-normalized scatter plot for weight w₀ with the associated linear regression in a solid line (other weights are reproduced in S2 Text).