**Shape:** The empirical distribution of a dataset.

**Input Dataset:** The dataset that differentially private algorithm is performed on to release information. For the task of releasing degree distribution, input dataset's true degree distribution is represented as a histogram.

**Output Dataset:** The resulting dataset after the differentially private algorithm has been performed on the original dataset. For the task of releasing degree distribution, output dataset's degree distribution is represented as a histogram.

**Epsilon:** The privacy parameter.

**Algorithm:** A differentially private algorithm for graphs.

**L1 Error:** The sum of the absolute difference between the true values and the noisy values.

**Degree Distrtibution:** The distriubtions of the degrees of the nodes in the graph.

**Triangle Counting:** A count of the number of triangle (A 3 node cycle) in the graph.

**2k-Triangle Counting:**A count of the number of 2 overlapping triangles (3 node cycles) in the graph.

**3k-Star Counting:** A count of the number of stars of size 3 (3 nodes connected to a central node) in the graph.

**4k-Clique Counting:** A count of cliques of size 4 in a graph. A clique is a set of vertices of a graph, where each pair is joined by an edge and no set containing this set has this property.