An edge-local differentially private algorithm counts arbitrary k-node graphlets with expected L2 error O(n^{k-1}), matching lower bounds for non-interactive methods and a Ω(n^{k-1.5}) bound for all methods.
Let the sets of nodes in each partition be U = {u1,...,u n/3}, Y = {y1,...,y n/3}, and W ={w1,...,w n/3}
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Counting Graphlets of Size $k$ under Local Differential Privacy
An edge-local differentially private algorithm counts arbitrary k-node graphlets with expected L2 error O(n^{k-1}), matching lower bounds for non-interactive methods and a Ω(n^{k-1.5}) bound for all methods.