Analysis of the Topological Structure and Evolutionary Path of Tujia Folk Song Melodic Profiles Based on Complex Networks

Tujia folk songs, as an important component of traditional Chinese music, have developed distinctive melodic structures through longterm oral transmission and intergenerational inheritance. From a signal-analysis perspective, their melodic contours can be regarded as discrete pitch-transition sequences, similar to the topological modelling of propagation paths in complex engineering networks. This study introduces complex network theory to model pitch movement in Tujia folk song melodies and constructs directed weighted networks for different historical periods and regional branches. A melodic database containing more than 200 Tujia folk songs was established, pitch sequences were extracted, and pitch-transition networks were formed. Topological indicators, including node degree, clustering coefficient, average path length, and modularity, were calculated to quantify the internal structural characteristics and evolutionary patterns of melodic contours. The results show that traditional branch folk songs exhibit high clustering coefficients and modularity, indicating stable local pitch movement habits and compact melodic structures. In contrast, modern adapted folk songs show lower network density, longer average path length, and increased randomness and diversity in pitch transitions. Evolutionary path analysis indicates that the melodic contours of Tujia folk songs have shifted from compact to discrete structures and from local constraints to greater global freedom. This topological transition reflects changes in transmission modes, aesthetic orientation, and creative concepts. The study offers a quantifiable framework for traditional music morphology and provides a signal-network analytical perspective that can also inform research on waveform structures, propagation topology, and complex signal systems.