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Title: Identification of Informative Core Structures in Weighted Directed Networks with Uncertainty Quantification

Abstract: In network analysis, noises and biases, which are often introduced by peripheral or non-essential components, can mask pivotal structures and hinder the efficacy of many network modeling and inference procedures. Recognizing this, identification of the core--periphery (CP) structure has emerged as a crucial data pre-processing step. While the identification of the CP structure has been instrumental in pinpointing core structures within networks, its application to directed weighted networks has been underexplored. Many existing efforts either fail to account for the directionality or lack the theoretical justification of the identification procedure. In this work, we seek answers to three pressing questions: (i) How to distinguish the informative and noninformative structures in weighted directed networks? (ii) What approach offers computational efficiency in discerning these components? (iii) Upon the detection of CP structure, can uncertainty be quantified to evaluate the detection? We adopt the signal-plus-noise model, categorizing different types of noninformative relational patterns, by which we define the sender and receiver peripheries. Furthermore, instead of confining the core component to a specific structure, we consider it complementary to either the sender or receiver peripheries. Based on our definitions on the sender and receiver peripheries, we propose spectral algorithms to identify the CP structure in directed weighted networks. Our algorithm stands out with statistical guarantees, ensuring the identification of sender and receiver peripheries with overwhelming probability. Additionally, we propose a hypothesis testing framework to infer CP structure upon detection. Our methods scale effectively for expansive directed networks. Implementing our methodology on faculty hiring network data revealed captivating insights into the informative structures and distinctions between informative and noninformative sender/receiver nodes across various academic disciplines.

This is a joint work with Wenqin Du, Tianxi Li, and Lihua Lei.