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Figure 3 | EPJ Data Science

Figure 3

From: Topology and evolution of the network of western classical music composers

Figure 3

Growth and evolution of the composer network. (A) The fundamental process of network growth. Our network grows when a CD is created (labeled ‘C’, left), bringing new composers (‘6’ and ‘7’) and/or new edges (dotted) into the projected network. (B) The evolution of the bipartite degree distribution. As the network grows the bipartite degree distribution converges to a power-law form \(p(q)\sim q^{-\gamma}\) with \(\gamma=1.89\pm0.01\) (solid line). The color of dots indicate the different timestamps (blue - 1990, green - 1995, red - 2000, cyan - 2005, violet - 2009). The plots are cumulative. (C) The growth behaviors of the number of edges and the degree of six highest-degree composers indicate the predictability of top-ranked composers. The number of edges in the CD-composer network (black square) and the bipartite degrees of six highest-degree nodes (colored) show an accelerating growth rate that appears to be quadratic (dotted curves). Assuming this behavior persists, in 2019 Mozart is projected to have \(q\simeq10\mbox{,}264\), JS Bach \(q\simeq9\mbox{,}211\), Beethoven \(q\simeq 8\mbox{,}119\), Brahms \(q\simeq5\mbox{,}162\), Verdi \(q\simeq4\mbox{,}897\) and Schubert \(q\simeq4\mbox{,}842\). (D) Estimating the non-linear preferential attachment exponent α. \(\rho>0\) indicates that the network exhibits a superlinear preferential attachment behavior, i.e. \(\Pi(k)\propto k^{\alpha}\) with \(\alpha>1\), where \(\Pi(k)\) is the probability that a node with degree k gets connected to a newly added link. The behaviors are observed for the majority of years (1990-1991, 1994 and 1997-2008), pointing out the disproportionately heavy concentration of new recordings onto the established composers.

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