Fig. 2
From: Machine learning meets complex networks via coalescent embedding in the hyperbolic space
Flow chart of the coalescent embedding algorithm. The algorithmic steps (grayscale squares) and the intermediate input/output (rounded red squares) of the coalescent embedding algorithm are illustrated. Each algorithmic step reports all the possible variants. The example network has been generated by the PSO model with parameters N = 50, m = 2, T = 0.1, γ = 2.5. We applied the RA1 pre-weighting rule and the ISO dimension reduction technique. The colors of the embedded nodes are assigned according to their angular coordinates in the original PSO network. Description of the variables in the mathematical formulas: x ij value of (i, j) link in adjacency matrix x; d i degree of node i; e i external degree of node i (links neither to CN ij nor to j); CN ij common neighbors of nodes i and j; V set of nodes; s,t any combination of network nodes in V; σ(s, t) number of shortest paths (s,t); \(\sigma \left( {s,t\left| {l_{ij}} \right.} \right)\) number of shortest paths (s, t) through link l ij ; N number of nodes; \(\zeta = \sqrt { - K}\), we set ζ = 1; K curvature of the hyperbolic space; \(\beta = \frac{1}{{\gamma - 1}}\) popularity fading parameter; γ exponent of power-law degree distribution. Details on each step are provided in the respective “Methods” sections
