Figure 1: Scientific Reports

Figure 1

From: Hidden geometries in networks arising from cooperative self-assembly

Figure 1

(a) Examples of geometrical shapes identified as cliques of the order q max  = 1, 2, 3, 4, from left to right. (b) Addition of a tetrahedron (q max  = 3) to the system of blue nodes can be nested in three different ways, i.e., by its face of the dimension q = 0, for instance, including the node “1”, q = 1, the link “3–6”, and q = 2, the triangle “4–5–6”. The corresponding number of new particles n a  = q max  + 1 − (q + 1) = q max q are shown by red nodes. (c) The number of simplexes Σ (t) as function of time for aggregation of poly-disperse cliques at different parameter ν. Lower panel shows the corresponding number n σ (t) of added simplexes per time step. Inset: Average growth rate RΣ ≡ 〈dΣ/dt〉 vs. ν. Bottom panels: Networks of aggregated cliques of sizes s [2,10] for the varied chemical potential ν = −9, ν = 0, and ν = +9, left to right. Different colours of nodes indicate the network’s community structure.