# A Combinatory Framework for Link Prediction in Complex Networks
## 8 Evaluation
### Random Geometric Network Comparable Tests
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{6}{c}{**Random Geometric Network Comparable Tests**} \\ \hline \multicolumn{6}{c}{**Test 1: Composition of Jaccard - cnc vs. Jaccard**} \\ \hline _Subgraph_ & \multicolumn{2}{c}{_Predictor Score_} & \multicolumn{2}{c}{_Best Basic Algorithm Score_} & \multicolumn{2}{c}{_Difference_} \\ _/AUC/Precision_ & \multicolumn{2}{c}{_/AUC/Precision_} & \multicolumn{2}{c}{_Difference_} \\ \hline Subgraph.0 (train set) & 772 & 0.9985 & 0.780 & 735 & 0.9995 & 0.743 & \(+\)37 more \\ \hline Subgraph.1 (test set) & 775 & 0.9975 & 0.762 & 740 & 0.9995 & 0.728 & \(+\)35 more \\ \hline Subgraph.2 (test set) & 813 & 0.9990 & 0.783 & 770 & 0.9985 & 0.742 & \(+\)43 more \\ \hline Subgraph.3 (test set) & 803 & 0.9985 & 0.746 & 753 & 0.9990 & 0.699 & \(+\)50 more \\ \hline Subgraph.4 (test set) & 787 & 0.9980 & 0.768 & 751 & 0.9985 & 0.733 & \(+\)36 more \\ \hline Subgraph.5 (test set) & 759 & 0.9990 & 0.752 & 721 & 1.0000 & 0.714 & \(+\)38 more \\ \hline \multicolumn{6}{c}{**Test 2: Composition of res_alloc - adamic_adar - Jaccard vs. res_alloc**} \\ \hline _Subgraph_ & \multicolumn{2}{c}{_Predictor Score_} & \multicolumn{2}{c}{_Best Basic Algorithm Score_} & \multicolumn{2}{c}{_Difference_} \\ _/AUC/Precision_ & \multicolumn{2}{c}{_/AUC/Precision_} & \multicolumn{2}{c}{_Difference_} \\ \hline Subgraph.0 (train set) & 774 & 1.0000 & 0.782 & 738 & 1.0000 & 0.746 & \(+\)36 more \\ \hline Subgraph.1 (test set) & 771 & 0.9985 & 0.758 & 756 & 0.9985 & 0.744 & \(+\)15 more \\ \hline Subgraph.2 (test set) & 804 & 0.9990 & 0.775 & 773 & 0.9995 & 0.745 & \(+\)31 more \\ \hline Subgraph.3 (test set) & 797 & 0.9985 & 0.740 & 771 & 1.0000 & 0.716 & \(+\)26 more \\ \hline Subgraph.4 (test set) & 784 & 1.0000 & 0.765 & 753 & 0.9965 & 0.735 & \(+\)31 more \\ \hline Subgraph.5 (test set) & 754 & 0.9980 & 0.747 & 732 & 0.9965 & 0.725 & \(+\)22 more \\ \hline \multicolumn{6}{c}{**Test 4: Composition of jacc - cnc - res_alloc - adam_dar - pref_attach vs. res_alloc**} \\ \hline _Subgraph_ & \multicolumn{2}{c}{_Predictor Score_} & \multicolumn{2}{c}{_Best Basic Algorithm Score_} & \multicolumn{2}{c}{_Difference_} \\ _/AUC/Precision_ & \multicolumn{2}{c}{_/AUC/Precision_} & \multicolumn{2}{c}{_Difference_} \\ \hline Subgraph.0 (train set) & 772 & 0.9980 & 0.780 & 738 & 1.0000 & 0.746 & \(+\)36 more \\ \hline Subgraph.1 (test set) & 773 & 0.9970 & 0.760 & 756 & 0.9985 & 0.744 & \(+\)17 more \\ \hline Subgraph.2 (test set) & 802 & 1.0000 & 0.773 & 773 & 0.9995 & 0.745 & \(+\)29 more \\ \hline Subgraph.3 (test set) & 802 & 0.9995 & 0.745 & 771 & 1.0000 & 0.716 & \(+\)31 more \\ \hline Subgraph.4 (test set) & 783 & 0.9980 & 0.764 & 753 & 0.9965 & 0.735 & \(+\)30 more \\ \hline Subgraph.5 (test set) & 757 & 0.9985 & 0.750 & 732 & 0.9965 & 0.725 & \(+\)25 more \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparable tests in random geometric network. From the pure random network we have created three sub networks. Like before, each of these has been derived by removing random edges from the original pure random network each time. Table 11 shows the number of edges removed as well as the performances of the network. \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{2}{c}{**Random Graph Properties**} \\ \hline Nodes & 620 \\ \hline Edges & 2950 \\ \hline Transitivity & 0.016 \\ \hline Average clustering & 0.017 \\ \hline Average shortest path length & 3.094 \\ \hline Network diameter & 5 \\ \hline Network efficiency & 0.344 \\ \hline The average local efficiency of the network & 0.018 \\ \hline Mean degree & 9.516 \\ \hline Degree Pearson Correlation coefficient & \(-\)0.013 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Random network properties. Figure 5: Random graph visualization and histograms. Here we present a visualization of pure random network, as well as the distribution of its node degrees in the form of a histogram. From the visualization and histograms, we can conclude that the network consists of nodes with links to each other uniformly distributed.