Fig. 3

Percolation on the RIGC. We demonstrate percolation on the example of Figure 1. From left to right, we trace back why percolation on the RIGC is another RIGC with a different community list. Leftmost, we randomly choose edges to delete from the resulting RIGC; we represent these edges as dotted. In the second subfigure, we trace back each edge of the RIGC to the corresponding edge within a community, as shown in the step before contracting the imaginary edges. In the third subfigure, we remove the percolated edges. Note that the individuals, their number of membership tokens, and where the tokens are matched, are unaffected. Communities that became disconnected due to removing edges are now replaced by their connected components, which we treat as separate communities. Rightmost, we recognize the matching for another RIGC, with the same list of individuals with the same number of membership tokens, and with the new (random) percolated community list