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Table 1 Algorithm of probability graph isomorphism judgment based on circuit simulation.

From: An novel frequent probability pattern mining algorithm based on circuit simulation method in uncertain biological networks

Algorithm: Isomorphism judgment Algorithm of probability graph IsomorphismCal (g α , g i , ε , θ)

Input: two probability graph g α and g i , the mismatch threshold value ε of the node voltage sequences set, the mismatch threshold value θ of probability adjoint matrix

Output: the bool value Iso of two graph isomorphism, the node mapping sequence Inje i , the mismatch value VMval i of node voltage sequences matrix

1. //Generate the node voltage sequence matrix S α , S i according to g α , g i

    For each graph in {g α , g i }

        generate associated circuit N α and N i

    End

    For each graph in {g α , g i }

        For j = 1 to k Calculate the node voltage sequence S j while set node j as reference node;

             S = S J S , S { S α , S i }

        End

  End

2. //calculate distance matrix according to S α , S i

    Calculate Dist(N α , N i ) according to formula(3);

3. //Get the node mapping relationship Inje i and the mismatch value of node voltage VMval i by Hungarian algorithm

    VMval i , Inje i > ← Hungarian(Dist);

4. // Compare VMval i and ε

    If VMval i <= ε

           g α and g i is not probability isomorphic;

      Continue;

    Else

        g α and g i maybe probability isomorphic; // g α and g i maybe probability isomorphic, and need further deal

5. //Calculate the mismatch value of adjoint matrix PMval i by adjust the adjoint matrix of g α and g i according to nodes mapping sequence

    If PMval i <= θ

         g α and g i is probability isomorphic;

         Iso =True;

         Return <Iso, Inje i ,VMval i > ;

  Else

         Return PermuteInjectedSequenceAndTestIso (g α , g i , Inje i , VMval i , θ);

         // Enumeration the node mapping relationship for isomorphic judgment

  End