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

Algorithm 2

GROUPING algorithm.

Input: a weighted graph 𝐺_𝑙.

Output: each vertex is assigned to a group.

Calculate the centrality score of each vertex 𝑣∈𝐺_𝑙,

Order 𝑣∈𝑉(𝐺_𝑙) via their centrality scores, such

that 𝑄=(𝑣₁,𝑣₂,…,𝑣_𝑛) with score(𝑣₁)≥score(𝑣₂)≥⋯≥score(𝑣_𝑛).

𝑖=0

while 𝑄≠∅

 𝑖=𝑖+1

 Create a new group 𝐶_𝑖=𝑣_𝑖1, where 𝑣_𝑖1 is the first vertex in the vertex queue 𝑄.

 New_𝑄=𝑄−𝑣_𝑖1

 while |New_𝑄|<|𝑄|

  𝑄=New_𝑄

  Find the candidate neighbor set  𝑁(𝐶_𝑖) of 𝐶_𝑖.

  Calculate the contribution to 𝐶_𝑖 of each vertex in 𝑁(𝐶_𝑖).

  Sort 𝑣∈𝑁(𝐶_𝑖) in descending order by their contribution to 𝐶_𝑖, that is,

  𝑄_𝑁=(𝑣_𝑛1,𝑣_𝑛2,…,𝑣_𝑛𝑘), where 𝑣_𝑛𝑖∈𝑁(𝐶_𝑖) and

   contribution(𝑣_𝑛1,𝐶_𝑖)≥contribution(𝑣_𝑛2,𝐶_𝑖)≥⋯≥contribution(𝑣_𝑛𝑘,𝐶_𝑖).

  if 𝑁(𝐶_𝑖)=∅, break.

  else

   𝐶_𝑖=𝐶_𝑖∪𝑣_𝑛1

   New_𝑄=𝑄−𝑣_𝑛1, 𝑄_𝑁=𝑄_𝑁−{𝑣_𝑛1}