A Modularity Degree Based Heuristic Community Detection Algorithm

Algorithm 1

Iteration procedure of MDBH algorithm.

Input: Adjacent matrix of network 𝐺

Output: Intermediate community detection result of 𝐺

  Step  1. Get community 𝑉_𝑛 which the current node 𝑖 belongs to, find the maximum

  value of 𝐿(𝑖,𝑉_𝑚), 𝑚∈{1,2,…,𝑁}. Suppose S to be the summation of the degree

  of all members’ in one community.

    IF  𝑚=𝑁, go to Step  3.

    IF more than one communities make 𝐿(𝑖,𝑉) be maximum are found

      Choose the community having the largest 𝑆 as 𝑉_𝑚. If more than one

      communities having the largest 𝑆 are found, randomly choose one as 𝑉_𝑚.

  Step  2. Calculate and determine the inequality (5) of (3𝐿(𝑖,𝑉_𝑚)−𝑑(𝑖))Num(𝑉_𝑚)>

  𝐸_in𝑉_𝑚−𝐸_out(𝑉_𝑚), if the inequality is true, then update the network as follows:

    (1) Delete node 𝑖 from the original community 𝑉_𝑛, and merge node 𝑖 into

    community 𝑉_𝑚, update Num(𝑉_𝑛)=Num(𝑉_𝑛)−1,Num(𝑉_𝑚)=Num(𝑉_𝑚)+1.

    (2) 𝐸_in(𝑉_𝑚)=𝐸_in(𝑉_𝑚)+𝐿(𝑖,𝑉_𝑚),𝐸_out(𝑉_𝑚)=𝐸_out(𝑉_𝑚)+𝑑(𝑖)−2𝐿(𝑖,𝑉_𝑚).

    (3) 𝐸_in(𝑉_𝑛)=𝐸_in(𝑉_𝑛)−𝐿(𝑖,𝑉_𝑛),𝐸_out(𝑉_𝑛)=𝐸_out(𝑉_𝑛)−𝑑(𝑖)+2𝐿(𝑖,𝑉_𝑛).

    (4) For each neighbor node 𝑘 of node 𝑖, let 𝐿(𝑘,𝑉_𝑛)=𝐿(𝑘,𝑉_𝑛)−1,

    𝐿(𝑘,𝑉_𝑚)=𝐿(𝑘,𝑉_𝑚)+1.

  Step  3. Traverse the network sequentially to get next node 𝑗, if 𝑗 exists, go to Step  1,

  else go to Step  4.

  Step  4. 𝑝=𝑝+1 and end of this iteration.