Preferential Attachment in Graphs with Affinities

Here, we give a full proof of Theorem 1. Recall that an equivalent construction of the PAGA graphs is obtained by collapsing the graph G 1 to G t m leading to t super nodes. Accordingly, based on G t m, we can directly generate G m by (temporarily) adding m more nodes, each linking with a single edge, and then collapsing these m nodes to the (t+ 1)th super node. Let dt,i(v) denote the degree of the super-node v after mt+ i− 1 edges have been introduced, the probability that the mt+ ith node (or equivalently its corresponding super-node t+ 1) connects to v is