Topology and evolution of the network of western classical music composers

EPJ Data Science

Table 1 Top 20 composers for degree, eigenvector, and betweenness centralities

Rank	Bipartite degree ( q )		Projected degree ( k )		Eigenvector centrality		Betweenness centrality
Rank	Name	Period	Name	Period	Name	Period	Name	Period
1	WA Mozart	C	JS Bach	B	JS Bach	B	JS Bach	B
2	JS Bach	B	WA Mozart	C	WA Mozart	C	WA Mozart	C
3	Beethoven	R	Handel	B	Handel	B	Handel	B
4	Brahms	R	Brahms	R	Brahms	R	Piazzolla	M
5	Schubert	R	Mendelssohn	R	Mendelssohn	R	Brahms	R
6	Verdi	R	Debussy	M	Schubert	R	Gershwin	M
7	Tchaikovsky	R	Schubert	R	Debussy	M	Debussy	M
8	R Schumann	R	Beethoven	R	Beethoven	R	Mendelssohn	R
9	Handel	B	Saint-Saëns	R	Saint-Saëns	R	Schubert	R
10	Wagner	R	Tchaikovsky	R	Tchaikovsky	R	Beethoven	R
11	Chopin	R	Ravel	M	Ravel	M	Villa-Lobos	M
12	Haydn	C	Gershwin	M	Fauré	R	Ravel	M
13	Liszt	R	R Schumann	R	R Schumann	R	Tchaikovsky	R
14	Mendelssohn	R	Fauré	R	Liszt	R	Copland	M
15	Debussy	M	Liszt	R	Chopin	R	Saint-Saëns	R
16	Puccini	R	Vivaldi	B	Vivaldi	B	Vivaldi	B
17	Vivaldi	B	Piazzolla	M	Rossini	R	Stravinsky	M
18	Dvor̆ák	R	Rossini	R	Rachmaninoff	M	Britten	M
19	Ravel	M	Chopin	R	Haydn	C	Hindemith	M
20	R Strauss	R	Verdi	R	Gershwin	M	Bernstein	M

Each centrality can be interpreted as representing distinct composer characteristics: The bipartite degree represents a composer’s popularity; the projected degree represents a composer’s compatibility with others; the eigenvector centrality is a generalization of the degree that considers the quality of connections (e.g. whether a composer tends to be paired with other prominent composers); the betweenness centrality measures how often a composer acts as an intermediary between two composers. Periods are abbreviated: Baroque (B), Classical (C), Romantic (R), and Modern (M).