## Appendix B _KS_ and _L2_ Statistics  
To measure the closeness of fit between the generated graphs and the input graph, we use a Kolmogorov-Smirnov (_KS_) test and the _L2_ (Euclidean) distance between the CCDFs for each of the statistics presented in Section 4. The model that generates graphs with the lowest _KS_ and _L2_ values has the closest fit to the real-world graph for that graph property.  
The _KS_ test is commonly used for goodness of fit and is based on the following statistic:  
\[KS=\sup|F^{*}(x)-S(x)| \tag{11}\]  
where \(F^{*}(x)\) is the hypothesised Cumulative Density Function (CDF) and \(S(x)\) is the empirical distribution function based on the sampled data [36]. As trying to perform a linear fit on a heavy-tailed distribution is biased [36], we use the logarithmic variant of the _KS_ test [14]:  
\[KS=\sup|\log F^{*}(x)-\log S(x)| \tag{12}\]  
We also calculate the _L2_ (Euclidean) distance for each statistic in the logarithmic scale:  
\[L2=\sqrt{\frac{1}{\log b-\log a}\sum_{x=a}^{b}(\log F^{*}(x)-\log S(x))^{2}} \tag{13}\]  
where \([a,b]\) is the support of distributions \(F^{*}(x)\) and \(S(x)\) respectively.  
Note that for the Singular Values and Primary Left Singular Vectors, we use the standard (linear) version of _KS_ and _L2_, as these statistics do not follow a heavy-tailed distribution.  
_B1. Real Attributes (Figures 5-8)_
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistic** & **Erdős-Rényi** & **MAG-R1** & **Agwan-R1 (GMM)** & **Agwan-R1 (BMM)** \\ \hline In-Vertex Strength & 5.679 & 4.912 & 2.244 & 1.507 \\ Out-Vertex Strength & 5.100 & 3.534 & 2.463 & 2.510 \\ Singular Values & 262,699.994 & 32,990.793 & 104,552.681 & 60,843.087 \\ Singular Vector & 69.775 & 74.606 & 8.842 & 4.884 \\ Clustering Coefficient (In-Edges) & 3.528 & 1.607 & 1.215 & 2.231 \\ Clustering Coefficient (Out-Edges) & 3.145 & 1.191 & 1.891 & 1.399 \\ Clustering Coefficient (6.949 & 1.438 & 0.813 & 1.033 \\ Triad Participation (Cycles) & 3.823 & 3.000 & 3.027 & 5.088 \\ Triad Participation (Middlemen) & 5.144 & 4.178 & 4.101 & 6.660 \\ Triad Participation (Ins) & 4.630 & 4.826 & 4.380 & 7.747 \\ Triad Participation (Outs) & 3.727 & 3.295 & 2.869 & 4.984 \\ \hline \hline \end{tabular}
\end{table}
Table 10: \(L2\) Statistic for Undirected Graph, Real Attributes.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Statistic**} & \multicolumn{3}{c}{**MAG**} & \multicolumn{3}{c}{**Agwan (GMM)**} \\ \cline{2-7}  & **L1** & **L5** & **L9** & **L1** & **L5** & **L9** \\ \hline In-Vertex Strength & 5.023 & 15.718 & 7.066 & 2.109 & 2.189 & 0.649 \\ Out-Vertex Strength & 3.001 & 10.882 & 3.737 & 2.483 & 2.060 & 0.988 \\ Singular Values & 29,286.029 & 44.305.501 & 22,485.397 & 111,282.298 & 72,433.178 & 5554.271 \\ Singular Vector & 68.345 & 24.388 & 66.319 & 7.932 & 5.224 & 5.763 \\ Clustering Coefficient (In-Edges) & 2.507 & 7.692 & 4.819 & 3.731 & 1.710 & 1.594 \\ Clustering Coefficient (Out-Edges) & 2.771 & & 5.642 & 2.785 & 1.501 \\ Clustering Coefficient & 2.450 & 13.922 & 7.653 & 8.296 & 2.617 & 1.827 \\ Triad Participation (Cycles) & 2.060 & 16.270 & 8.763 & 9.561 & 3.990 & 1.777 \\ Triad Participation (Middemen) & 2.828 & 18.575 & 11.150 & 10.101 & 6.094 & 2.476 \\ Triad Participation (Ins) & 3.293 & 16.361 & 13.740 & 14.168 & 6.562 & 3.074 \\ Triad Participation (Outs) & 1.459 & 14.603 & 6.315 & 9.218 & 3.960 & 2.077 \\ \hline \hline \end{tabular}
\end{table}
Table 8: _L2_ Statistic for Directed Graph, Synthetic Attributes.