A Multidimensional and Multimembership Clustering Method for Social Networks and Its Application in Customer Relationship Management

Algorithm 1

Input: A graph 𝐺=(𝑉;𝜔₁,𝜔₂,…,𝜔_𝑟) is a multi-weighted graph with 𝜔_𝑘: 𝐸(𝐺)↦[0,1].

Output: Meaningful community sets in 𝐺.

Algorithm: Detect Δ-quasi-cliques in 𝐺 with various levels of Δ, and construct a hierarchically nested system to illustrate their

inclusion relation.

While 𝐸(𝐺)≠∅

 begin

 determine the value of 𝑀₀

  Decompose(𝐺,𝑀₀)

 𝐸₀={𝑒∈𝐸(𝐺)∶𝜔_𝑘(𝑒)≥𝑀₀, 𝑘=1,2,…,𝑟}

 for each edge in 𝐸₀ in decreasing order of weights, if the two vertexes of edge are not in any community, create a new empty

 community 𝐶 Choose 𝑣 in the rest vertex sets that have maximum contribution to 𝐶 and add 𝑣 in it.

  Merging (𝐺)

 Merge two communities according to their common vertexes;

 Contract each community to a vertex and redefine the weight of the corresponding edges.

 Store the resulted graph to 𝐺.

 End.