Louvain algorithm: self-loop weight is double? In the 2nd phase of the Louvain algorithm, self-loops are given by the sum of all the intra-community weights. I'm wondering from their own figure, why all of the self-loops seem to have 2w weights, rather than w. Note in the blue community for instance: 2 intra-community edges, self loop has weight 4.
Every edge has the same weight, which it contributes to each endpoint. When both endpoints are in the same cluster, the edge counts twice towards that cluster. Then they are in different clusters, the edge counts once towards each of the two clusters. So each edge has the same overall contribution.