# A Hierarchical Orthographic Similarity Measure for Interconnected Texts Represented by Graphs
## 4 Representing a Textual Corpus as a Graph
### Graph Representation of a Textual Corpus
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Similarity Parameters**} & \multirow{2}{*}{**Threshold \(\alpha\)**} & \multicolumn{3}{c}{**Verses**} & \multicolumn{3}{c}{**Epigrams**} \\ \cline{3-8}  & & **Precision** & **Recall** & **F\({}_{1}\)-Score** & **Precision** & **Recall** & **F\({}_{1}\)-Score** \\ \hline \multirow{8}{*}{**Default**} & 0.1 & 0.1627 & 0.9984 & 0.2797 & 0.1638 & 0.9904 & 0.2811 \\  & 0.2 & 0.4305 & 0.9932 & 0.6007 & 0.5387 & 0.9741 & 0.6937 \\  & 0.3 & 0.8831 & 0.9831 & 0.9304 & 0.5741 & 0.9499 & 0.7156 \\  & 0.4 & 0.9609 & 0.9715 & 0.9661 & 0.6049 & 0.9147 & 0.7283 \\  & 0.5 & 0.9782 & 0.9417 & 0.9596 & 0.6687 & 0.8589 & 0.7520 \\  & 0.6 & 0.9986 & 0.8688 & 0.9292 & 0.7745 & 0.7757 & 0.7751 \\  & 0.7 & **1.0000** & 0.7452 & 0.8540 & 0.8559 & 0.6796 & 0.7576 \\  & 0.8 & **1.0000** & 0.6059 & 0.7546 & 0.8786 & 0.5599 & 0.6840 \\  & 0.9 & **1.0000** & 0.3398 & 0.5072 & 0.9365 & 0.3778 & 0.5384 \\ \hline \multirow{8}{*}{**Custom 1**} & 0.1 & 0.1455 & **1.0000** & 0.2540 & 0.0889 & 0.9998 & 0.1632 \\  & 0.2 & 0.2112 & 0.9951 & 0.3485 & 0.3515 & 0.9829 & 0.5178 \\  & 0.3 & 0.6899 & 0.9910 & 0.8135 & 0.5636 & 0.9574 & 0.7095 \\  & 0.4 & 0.9518 & 0.9833 & 0.9673 & 0.5992 & 0.9318 & 0.7294 \\  & 0.5 & 0.9718 & 0.9621 & 0.9669 & 0.6492 & 0.8923 & 0.7518 \\  & 0.6 & 0.9978 & 0.8980 & 0.9453 & 0.7424 & 0.8123 & 0.7758 \\  & 0.7 & 0.9999 & 0.7885 & 0.8817 & 0.8759 & 0.7187 & **0.7896** \\  & 0.8 & **1.0000** & 0.6442 & 0.7836 & 0.8895 & 0.5977 & 0.7150 \\  & 0.9 & **1.0000** & 0.3643 & 0.5340 & **0.9731** & 0.4354 & 0.6016 \\ \hline \multirow{8}{*}{**Custom 2**} & 0.1 & 0.1447 & **1.0000** & 0.2529 & 0.0798 & **1.0000** & 0.1478 \\  & 0.2 & 0.1502 & **1.0000** & 0.2611 & 0.0998 & 0.9998 & 0.1815 \\ \cline{1-1}  & 0.3 & 0.3028 & 0.9948 & 0.4642 & 0.5155 & 0.9800 & 0.6756 \\ \cline{1-1}  & 0.4 & 0.8616 & 0.9895 & 0.9211 & 0.5727 & 0.9562 & 0.7163 \\ \cline{1-1}  & 0.5 & 0.9633 & 0.9777 & **0.9704** & 0.6041 & 0.9236 & 0.7305 \\ \cline{1-1}  & 0.6 & 0.9854 & 0.9343 & 0.9592 & 0.6555 & 0.8634 & 0.7452 \\ \cline{1-1}  & 0.7 & 0.9995 & 0.8576 & 0.9231 & 0.7255 & 0.7954 & 0.7588 \\ \cline{1-1}  & 0.8 & **1.0000** & 0.7065 & 0.8280 & 0.8834 & 0.6882 & 0.7737 \\ \cline{1-1}  & 0.9 & **1.0000** & 0.4253 & 0.5968 & 0.8873 & 0.5352 & 0.6677 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental results of the first experiment using the proposed similarity measure. The employed parameter sets are listed in Table 1. The highest scores for each column are indicated in bold. In the case of verses, we observe the same trend across all three parameter sets. For low \(\alpha\) values, we find a very high recall but a very low precision. This suggests that (nearly) all similar texts are detected, albeit at the expense of misclassifying numerous text pairs as similar. With high \(\alpha\) values, we observe the reverse scenario, coupled with a slightly higher F\({}_{1}\)-score. The peak overall performance for verses is achieved with the third, most tolerant parameter set (i.e., the second custom parameter set) and an \(\alpha\) threshold of 0.5. For epigrams, the resulting values are generally lower in comparison to verses, yet the same trend can be observed across the three parameter sets. The lower scores are explained by the fact that these epigrams can structurally vary in more ways than the individual verses, coupled with the increased potential for orthographic inconsistencies in longer texts. Overall, the best score for the epigram test set is achieved by using the second set of parameters with an \(\alpha\) value of 0.7. In general, the choice of the hierarchical decomposition of a text and the parameters choices for each level in the hierarchical computation of the similarity can significantly influence the performance of the similarity measure. The high customisability of the proposed method provides the flexibility to fine-tune numerous parameters when determining the optimal parameter set for a given corpus.