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

Algorithm 3

MERGING algorithm.

Input: a weighted graph 𝐺_𝑙 which has already been

clustered into 𝑠 groups as in the GROUPING algorithm.

Output: each vertex is assigned to a new group.

List all groups of 𝐺_𝑙 as 𝐿={𝐶₁,𝐶₂,…,𝐶_𝑠} such

that 𝑉(𝐶₁)≥𝑉(𝐶₂)≥⋯≥𝑉(𝐶_𝑠)

 ℎ=2,𝑗=1

 while 𝑗<ℎ

  if 𝐶_𝑗∩𝐶_ℎ≥12∗min𝐶_𝑗,𝐶_ℎ,

   𝐿=𝐿∪𝐶_𝑗∪𝐶_ℎ−𝐶_𝑗−𝐶_ℎ

   𝑠=𝑠−1,ℎ=max{ℎ−2,1},

   ℎ=ℎ+1,𝑗=1

  else

   𝑗=𝑗+1