A Node Influence Based Label Propagation Algorithm for Community Detection in Networks

Algorithm 1

Label propagation algorithm for community detection in networks (LPA).

Input: 𝐺=(𝑉,𝐸).

Output: the result of community detection.

(1) Initialization: assign a unique label to each node in the network, 𝑐_𝑖(0)=𝑖.

(2) Iteration of label propagation:

 (a) Set 𝑡=1;

 (b) Arrange the nodes of the network in random order, and store the results in the vector 𝑋.

 (c) For each node 𝑣_𝑖∈𝑋,let𝑐_𝑖(𝑡)=𝑓(𝑐_𝑖1(𝑡),…,𝑐_𝑖𝑚(𝑡),𝑐_𝑖(𝑚+1)(𝑡−1),…,𝑐_𝑖𝑘(𝑡−1)), where 𝑣_𝑖1,…,𝑣_𝑖𝑚 are

neighbors of 𝑣_𝑖 those have already been updated in the current iteration and 𝑣_𝑖(𝑚+1),…,𝑣_𝑖𝑘 are

neighbors those are not yet updated in the current iteration. The function 𝑓 here returns the label

that the maximum number of its neighbors has. If multiple labels simultaneously have the

maximum number, then randomly select one of them to assign to the node.

 (d) If the label of every node does not change anymore, then stop the algorithm. Else, set 𝑡=𝑡+1 and go to Step (b).

(3) Community division: divide all nodes share the same label into a community; the type of labels

indicates the number of communities.