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

Algorithm 2

Node influence based label propagation algorithm for community detection in networks (NIBLPA).

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) Calculate the node influence value for each node and arrange nodes in descending order of NI

storing the results in the vector 𝑋.

(3) Iteration of label propagation:

 (a) Set 𝑡=1;

 (b) 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 that have already been updated in the current iteration and 𝑣_𝑖(𝑚+1),…,𝑣_𝑖𝑘 are

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

the maximum number of their neighbors has. If multiple labels simultaneously contained by the

greatest number of nodes, then we recalculate each of the values of labels contained by greatest

number nodes according to (5) and choose the label with maximum value to assign to the node 𝑣_𝑖.

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

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

indicates the number of communities.