Table 2 Algorithm of frequent probability pattern by two-step hierarchical clustering.

1. Initilize the n graphs {g₁,...,g_n}as the n leaves of cluster tree ;

2.  While Change_label!=0

3.     Change_label = 0; // Change_label indicates whether the process of merging clustering operation

4.     L_c = size(ResidentGraph); //Calculation subgraph number, L_c represents the total number of clusters

5.     For i= 1 to L_c /2

6.         <Iso,inje,VMval>=IsomorphismCal(g_i, g_{i+ L c /2}, ε, θ);

        // Determine g_i, g_{i+ L c /2}probability isomorphic

7.         If Iso= =TRUE

8.             g_i = union(g_i, g_{i+ L c /2});

9.             Change_label ++;

10.             ResidentGraph = {ResidentGraph i}; //if isomorphic, retaining only the subgraph label i to ResidentGraph

11.             Else

            ResidentGraph = {ResidentGraph i i+ L _c /2};//if not isomorphic, retaining only the subgraph label i, i+ L _c /2 to ResidentGraph

12.         End if

13.     End for

14.     End while

15.         SimpleHierarchicalClusteringForFrequentSubgraphWithPro(ResidentGraph, ε, θ ,freq);

//using a simple hierarchical clustering for the remaining probability subgraphs

16.         Calculate the probability isomorphic frequency p of the residual clusters g_r ;