Network analysis, especially through models like Exponential Random Graph Models (ERGMs), is crucial in understanding how musical styles, trends, and cultural influences diffuse through networks of musicians. However, ERGMs often face challenges like degeneracy, particularly when analyzing higher-order patterns within these networks. The Latent Order Logistic Regression (LOLOG) model provides an alternative by modeling connections as they form sequentially, which helps avoid degeneracy. To further enhance this model, we propose incorporating triadic independency, wherein we can capture more complex relationships in musical collaborations, offering deeper insights into how cultural information spreads and evolves within these networks. This enhanced model is being tested on networks of Australian musicians to assess its effectiveness in tracing collaboration patterns and enhancing music information retrieval, while also reflecting the cultural dynamics within these communities.