# Interactive Graph Stream Analytics in Arkouda
## 7 Experiments
### Datasets Description and Analysis  
We will use graph files and read the edges line by line to simulate the sliding window of a graph stream. The graphs selected for testing were chosen from various publicly available datasets for the benchmarking of graph methods. These include datasets from the 10 th DIMACS Implementation Challenge [40], as well as some real-life graph datasets from the Stanford Network Analysis Project (SNAP) [[http://snap.stanford.edu/data/](http://snap.stanford.edu/data/)]([http://snap.stanford.edu/data/](http://snap.stanford.edu/data/)) (accessed on 20 July 2021). Pertinent information about these datasets for the triangle counting method are displayed in Table 3.  
Based on the graphs' degree distribution, we divided them into two classes, normal distribution and power law distribution. Prior research has shown that some real-world graphs follow power law distributions. Normal distributions are also found ubiquitously  
\begin{table}
\begin{tabular}{c l l l l l} \hline
**Degree Distribution** & **Graph Name** & **Edges** & **Vertices** & **Mean** & **Standard Deviation** \\ \hline \multirow{8}{*}{Normal} & delaunay\_n10 & 3056 & 1024 & 5.96875 & 3.10021 \\ \cline{2-6}  & delaunay\_n11 & 6127 & 2048 & 5.98340 & 3.76799 \\ \cline{2-6}  & delaunay\_n12 & 12,264 & 4096 & 5.98828 & 3.49865 \\ \cline{2-6}  & delaunay\_n13 & 24,547 & 8192 & 5.99292 & 3.25055 \\ \cline{2-6}  & delaunay\_n14 & 49,122 & 16,384 & 5.99634 & 3.30372 \\ \cline{2-6}  & delaunay\_n15 & 98,274 & 32,768 & 5.99817 & 3.37514 \\ \cline{2-6}  & delaunay\_n16 & 196,575 & 65,536 & 5.99899 & 3.35309 \\ \cline{2-6}  & delaunay\_n17 & 393,176 & 131,072 & 5.99938 & 3.26819 \\ \cline{2-6}  & delaunay\_n18 & 786,396 & 262,144 & 5.99972 & 3.2349 \\ \hline
**Degree Distribution** & **Graph Name** & **Edges** & **Vertices** & \(a\) & \(k\) \\ \hline \multirow{8}{*}{power law} & amazon & 925,872 & 334,863 & 1,920,877 & 2.81 \\ \cline{2-6}  & dblp & 1,049,866 & 317,080 & 3,299,616.65 & 2.71 \\ \cline{2-6}  & youtube & 2,987,624 & 1,134,890 & 701,179.83 & 1.58 \\ \cline{2-6}  & lj & 34,681,189 & 3,997,962 & 50,942,065.49 & 2.40 \\ \cline{2-6}  & orkut & 117,185,083 & 3,072,441 & 40,351,890.91 & 2.12 \\ \cline{2-6}  & ca-HepTh & 51,971 & 9877 & 23,538.9 & 2.29 \\ \cline{2-6}  & ca-CondMat & 186,936 & 23,133 & 68,923.6 & 2.23 \\ \cline{2-6}  & ca-AstroPh & 396,160 & 18,772 & 46,698.3 & 1.84 \\ \cline{2-6}  & email-Enron & 367,662 & 36,692 & 10,150.2 & 1.54 \\ \cline{2-6}  & ca-GrQc & 28,980 & 5242 & 6610.35 & 2.04 \\ \cline{2-6}  & ca-HepPh & 237,010 & 12,008 & 4601.72 & 1.44 \\ \cline{2-6}  & loc-brightkite\_edges & 214,078 & 58,228 & 44,973.1 & 1.88 \\ \hline \end{tabular}
\end{table}
Table 3: Graph benchmarks utilized for the triangle counting algorithm.  
in the natural and social sciences to represent real-valued random variables whose distributions are not known. For normal distributions, their typical parameters, the mean and standard deviation fitted from the given graphs, are listed in Table 3 too. Figure 5 shows the comparison between the fitting results and the original graph data. We can see that the fitting results can match with the original data very well. In other words, the Delaunay graphs follow the normal distribution.  
For graphs that follow the power law distribution \(y(x)=a\times x^{-k}\), we also present their fitting parameters \(a\) and \(k\) in Table 3. Figure 6 provides some examples of these graphs. We can see that, in general, their signatures are close to power laws. However, we can also see that some data do not fit a power law distribution very well.