## 4 Results
### Obtained Results--General Comparison of Tracks and Genres  
Network representations were calculated for each compared pair of pieces. Then, in each case, a vertex adjacency matrix, a matrix describing the weights on the edges existing between individual vertices, as well as the vertex weight vectors of both networks were calculated. For structures compared in this way, the values described in Section 3.2 were calculated, and subsequently the matrix of the optimal assignment of vertices from one structure to another was calculated using the meta-criterion. For the assignment calculated in this way, the value of the objective function is also calculated--a measure of the similarity of pieces. An example result is presented in Figure 3.  
\begin{table} \begin{tabular}{c c c c c c} \hline
**Piece Title** & 1N1 & 1 \(V_{\textbf{NI}}\) l & 1E1 & \(\omega(\textbf{G})\) & \(Deg_{\textit{agg}}(\textbf{G})\) \\ \hline _Canon in \(D\)_ & 687 & 9 & 50 & 0.30 & 5.56 \\ \hline _Nocturne Op. 9_ & 489 & 12 & 80 & 0.48 & 6.67 \\ \hline _Shchedryk_ & 636 & 10 & 37 & 0.22 & 3.70 \\ \hline _Tocata and Fugue_ & 1851 & 13 & 118 & 0.70 & 9.08 \\ \hline _Für Elise_ & 618 & 13 & 75 & 0.44 & 5.77 \\ \hline _Ode to Joy_ & 62 & 5 & 15 & 0.09 & 3.00 \\ \hline _Godfather_ & 309 & 10 & 40 & 0.24 & 4.00 \\ \hline _Harry Potter_ & 60 & 11 & 27 & 0.16 & 2.45 \\ \hline _Reuqiem for a Dream_ & 377 & 7 & 18 & 0.11 & 2.57 \\ \hline _The Hobbit_ & 135 & 7 & 27 & 0.16 & 3.86 \\ \hline _Thinking Out Loud_ & 413 & 8 & 37 & 0.22 & 412 \\ \hline _My Way_ & 288 & 11 & 56 & 0.33 & 5.09 \\ \hline _L UEFA Champions League theme (vocal part)_ & 36 & 8 & 19 & 0.11 & 2.38 \\ \hline _LIFEA Champions League theme (violin part)_ & 206 & 10 & 49 & 0.29 & 4.90 \\ \hline _Rolling in the Deep_ & 657 & 8 & 35 & 0.20 & 4.38 \\ \hline _Yesterday_ & 211 & 10 & 32 & 0.19 & 3.20 \\ \hline _Yellow Submarine_ & 355 & 10 & 39 & 0.23 & 3.90 \\ \hline _The Final Countdown_ & 775 & 9 & 43 & 0.25 & 4.78 \\ \hline _Nothing Else Matters_ & 883 & 10 & 52 & 0.30 & 5.20 \\ \hline _Numb_ & 403 & 8 & 34 & 0.20 & 4.25 \\ \hline _We Will Rock You_ & 240 & 7 & 31 & 0.18 & 4.43 \\ \hline \end{tabular}  Description: \(|N|\)—cardinality of the set of notes of the piece, \(|V_{\textit{NI}}|\)—cardinality of the set of non-isolated graph vertices, \(|E|\)—cardinality of the set of graph edges, \(\omega(G)=\frac{|E|}{|V|^{2}}\)—graph density (where \(|V|\)—cardinality of the set of all graph vertices), \(Deg_{\textit{agg}}(G)\)—average vertex degree. \begin{tabular}{c cThe obtained results were sorted by the genres of the pieces. The original pieces and their arrangements were also compared separately. In Tables 2-6, four comparison values are presented in each of the cells, respectively:  
1. the value obtained using the arithmetic mean of the criteria (scalarization using the meta-criterion in the form of a weighted average of criteria with equal weights of 0.333),
2. structural similarity value,
3. vertex quantitative similarity value,
4. edge similarity value. To increase the readability, Tables 2-6 ignore the comparison of the piece with itself (each piece is, by definition, maximally similar to itself), and only the lower triangular matrix is supplemented (distances meet the relation \(dist(a,b)=dist(b,a)\), hence every matrix is symmetric). The adopted domain and the interpretation of the values of individual criteria are described in Section 3.4. Table 2 presents the results of measurements of the distance between pieces representing classical music. It is worthwhile to note that the piece _Tocata and Fugue_ is characterized by very low similarity values in relation to all other pieces. This is due to its far more extended structure compared to other compositions. As shown in Table 1, this piece consists of almost 2000 notes, and this is 2-3 times longer than the others. Furthermore, this piece uses all the notes in the octave and almost all possible connections between them--the graph density is very high as for the graphs of musical pieces and amounts to 0.7.