1 Function next_popular_vertex (N, Step,Exclude_destinations[ ])

│ // This function returns the identifier id of a vertex

│ // the vertex not included in the vector Exclude_destinations[0::Step - 1] if Step > 0

│ // This identifier is a random value smaller than N and

│ // it is generated with probability: $Prob\left(id\right)=\frac{2^{N-id}}{{\displaystyle {\sum }_{j=1}^N{2}^{N-j}}}$

2 │ id ß prob_rand(N; Prob;Exclude_destinations[ ]).

3 └ return id

// N is the total amount of Vertices in the community

4 Function Generator (N, Length_paths, Total_paths)

│ // This function defines the edges and weights of a single community

5 │ for Source = 0 à N do

6 │ │ for Destination = 0 à N do

7 │ │ │ edge_weight[Source][Destination] ß 0

8 │ for X = 0 à Total_paths do

9 │ │ for Step = 0 à Length_paths do

10 │ │ │ if Step == 0 then

11 │ │ │ └ Path[Step] ß next_popular_vertex(N, Step, Ø)

12 │ │ │ else if Step > 0 then

13 │ │ │ │ Path[Step] ß next_popular_vertex(N; Step; Path[ ])

14 │ │ │ │ Previous_v ß Path[Step - 1]

15 │ │ │ │ Current_v ß Path[Step]

16 └ └ └ └ edge_weight[Previous_v][Current_v]+=1=(2^Step)