Fig. 1: Geometric renormalization of weights (GRW). | Communications Physics

Fig. 1: Geometric renormalization of weights (GRW).

From: Geometric renormalization of weighted networks

Fig. 1: Geometric renormalization of weights (GRW).The alternative text for this image may have been generated using AI.

Each layer is obtained after a GRW step with resolution r starting from the original network in l = 0. Each node i in red is placed at an angular position on the similarity circle and has a size proportional to the logarithm of its hidden degree. Straight solid lines represent the links in each layer with weights denoted by their thickness. Coarse-graining blocks correspond to the blue shadowed areas, and dashed lines connect nodes to their supernodes in layer l + 1. Two supernodes in layer l + 1 are connected if and only if some node of one supernode in layer l is connected to some node of the other, with the supremum among the weights of links between the constituent nodes as the weight of the new connection (dark blue links give an example). The GRW transformation has semigroup structure with respect to the composition. In the figure, the transformation with r = 4 goes from l = 0 to l = 2 in a single step.

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