  Hub structure, characterized by a few highly interconnected nodes surrounded
by a larger number of nodes with fewer connections, is a prominent topological
feature of biological brains, contributing to efficient information transfer
and cognitive processing across various species. In this paper, a mathematical
model of hub structure is presented. The proposed method is versatile and can
be broadly applied to both computational neuroscience and Recurrent Neural
Networks (RNNs) research. We employ the Echo State Network (ESN) as a means to
investigate the mechanistic underpinnings of hub structures. Our findings
demonstrate a substantial enhancement in performance upon incorporating the hub
structure. Through comprehensive mechanistic analyses, we show that the hub
structure improves model performance by facilitating efficient information
processing and better feature extractions.
