Exploring the Entropy Complex Networks with Latent Interaction

In the present work, we study the introduction of a latent interaction index, examining its impact on the formation and development of complex networks. This index takes into account both observed and unobserved heterogeneity per node in order to overcome the limitations of traditional compositional similarity indices, particularly when dealing with large networks comprising numerous nodes. In this way, it effectively captures specific information about participating nodes while mitigating estimation problems based on network structures. Furthermore, we develop a Shannon-type entropy function to characterize the density of networks and establish optimal bounds for this estimation by leveraging the network topology. Additionally, we demonstrate some asymptotic properties of pointwise estimation using this function. Through this approach, we analyze the compositional structural dynamics, providing valuable insights into the complex interactions within the network. Our proposed method offers a promising tool for studying and understanding the intricate relationships within complex networks and their implications under parameter specification. We perform simulations and comparisons with the formation of Erdös-Rényi and Barabási-Alber-type networks and Erdös-Rényi and Shannon-type entropy. Finally, we apply our models to the detection of microbial communities.