“Follow the Leader”: A Centrality Guided Clustering and Its Application to Social Network Analysis

Algorithm 4

CONTRACTION algorithm.

Input: a weighted graph 𝐺_𝑙 which has already been

merged into 𝑠 groups as in the MERGING algorithm,

Output: a contracted graph with edge weights.

List all groups of 𝐺_𝑙 after the MERGING step as 𝐿={𝐶₁,𝐶₂,…,𝐶_𝑠}

Generate a new vertex 𝑣_𝑝 to represent the group 𝐶_𝑝.

for 𝑖=1 to 𝑠

 for 𝑗=1 to 𝑖

  𝑤𝑣_𝑖,𝑣_𝑗=∑_{𝑒∈𝐸(𝐶𝑖,𝐶𝑗)}𝑤(𝑒)𝑉𝐶_𝑖∗𝑉𝐶_𝑗

  𝑤𝑣_𝑗,𝑣_𝑖=𝑤𝑣_𝑖,𝑣_𝑗