Algorithm 1.

Frequent Subgraph Identification

Input:
	Graph database D; Threshold θ; Privacy budget ϵ2; Maximum size of frequent subgraphs Mg;
Output:
	Frequent subgraphs F;
1:	F ← ∅; ${ϵ}_b=\frac{\alpha {ϵ}_2}{M_g}$; ${ϵ}_c=\frac{(1-\alpha ){ϵ}_2}{M_g}$;
2:	for i from 1 to Mg do
3:	Ci ← generate the set of candidate i-subgraphs;
4:	count the support of each candidate i-subgraph;
5:	ni = binary_estimation(Ci, ϵb, θ);\\see Sec. 6.1
6:	Fi = conditional_exponential(Ci, ϵc, θ, ni);\\see Sec. 6.2
7:	F += Fi;
8:	end for
9:	return F;