A Multilevel Simplification Algorithm for Computing the Average Shortest-Path Length of Scale-Free Complex Network

Algorithm 1

Calculate the ASPL of 𝐺 from the simplified graph 𝐺^′.

(1) for 𝑖 in 𝐺^′

(2)  for 𝑗 in 𝐺^′:

(3)  if (𝑖 <> 𝑗):

(4)   Number_of_Path_of_𝐺^′++

(5)   Length = Shortest_Path_Length(𝑖,𝑗)

(6)   Length_of_𝐺^′ += Length

(7)   if is_connector(𝑗):

(8)   Number_of_Path_to_Connector += Number_of_suspension_edges_of(𝑗)

(9)   Length_to_Connector += Length * Number_of_suspension_edges_of(𝑗)

(10) Length_of_𝐺 = Length_of_𝐺^′ + Length_to_Connector + Number_of_Path_to_Connector + Number_of_𝑠_nodes

(11) Number_of_path_of_𝐺 = Number_of_Path_of_𝐺^′ + Number_of_Path_to_Connector + Number_of_𝑠_nodes