The Application of Mathematical Modeling and Graph Theory in Musical Research

We create an information database for 5602 excellent artists based on “Inluence _data” scraped from AllMusic.com, which contains almost all relating information of an artist. Later, the networks and sub-networks with artists and genres are established, from which we find the connections between artists and genres, and find that the network has the characteristics of ‘central effect’. Besides, in order to better explain the connections between artists through the networks, we established the Musical Influence Model. In this model, we correct the number of influencers (IN) and the number of followers (FN) of each artist based on their changing characteristics over time. For IN, we correct it according to the radical function family. For FN, we correct it according to the Population Logistic Model. Besides, we develop probability coefficient (b) to correct the total number of actual influencers and followers based on genre. Based on the Music Influence Model, we can obtain the music influence ranking list among a certain range.