An Algorithm for Finding Functional Modules and Protein Complexes in Protein-Protein Interaction Networks

Algorithm 2

ExtendNearClique.

(1) for all node 𝑁∈𝐺 do

(2)  if (𝑁.𝑐𝐼𝑑𝑥=0) then {find node outside the clique}

(3)   𝑞𝐶𝑙𝑖𝑞𝑢𝑒𝐶𝑛𝑡𝑠=∅ { 𝑞𝐶𝑙𝑖𝑞𝑢𝑒𝐶𝑛𝑡𝑠 the number of edges, which the node N connected with different near-cliques}

(4)   for all edge 𝐸∈𝑁 do

(5)    if (𝐸.target.𝑐𝐼𝑑𝑥>0) then

(6)     𝑞𝐶𝑙𝑖𝑞𝑢𝑒𝐶𝑛𝑡𝑠[𝐸.target.𝑐𝐼𝑑𝑥]++

(7)    end if

(8)   end for

(9)   𝑞𝐶value=0 {initialize 𝑐𝐼𝑑𝑥 of node N}

(10)   for all (𝑐∈𝑞𝐶𝑙𝑖𝑞𝑢𝑒𝐶𝑛𝑡𝑠) do

(11)    if ((𝑐>1) and indegree(𝑥,𝐺^′)≥outdegree(𝑥,𝐺^′)) or ((𝑐>1) and indegree(𝑥,𝐺^′)≥0.5∗|𝐺^′|) then {a node

         outside a clique interacts with multiple nodes in the clique, and either indegree(𝑥,𝐺^′)≥outdegree(𝑥,𝐺^′) or

         indegree(𝑥,𝐺^′)≥0.5∗|𝐺^′|) is true}

(12)     if (𝑞𝐶value>0) then

(13)      for all 𝑡𝑚𝑝𝑁∈𝐺 do

(14)       if (𝑡𝑚𝑝𝑁.𝑐𝐼𝑑𝑥=𝑞𝐶value) then

(15)        𝑡𝑚𝑝𝑁.𝑐𝐼𝑑𝑥=𝑞𝐶value {near-clique of type C}

(16)       end if

(17)      end for

(18)     else

(19)      𝑞𝐶value=𝑐 {near-clique of type A}

(20)     end if

(21)    end if

(22)   end for

(23)   𝑁.𝑐𝐼𝑑𝑥=𝑞𝐶value {assign 𝑞𝐶value to node 𝑁 as its 𝑐𝐼𝑑𝑥}

(24)  end if

(25) end for