homophily measurement

This study investigates how homophily—the tendency of individuals to form ties with similar others—drives network evolution and exacerbates structural inequality in social networks. Methodologically, it pioneers the extension of homophily modeling to higher-order network structures, including hypergraphs and simplicial complexes, and introduces a tunable generative framework that integrates network science, graph theory, and statistical modeling to quantitatively characterize multi-level social connections. Key contributions include: (i) establishing a unified analytical framework for homophily that uncovers the co-evolutionary dynamics of intra-group reinforcement and inter-group segregation; (ii) empirically validating that this mechanism shapes information diffusion bias and resource allocation inequality in real-world networks; and (iii) providing an interpretable theoretical foundation for designing fair algorithms, community governance strategies, and targeted network interventions.

This paper addresses representational bias against minority groups in network centrality ranking caused by missing edges. We first formally define “minority group representation” and propose a group-dependent edge-missing error model. Based on this model, we develop a statistical testing framework to detect ranking bias and design an asymptotically consistent correction method that jointly optimizes fairness and ranking accuracy. Our approach integrates centrality measures, stochastic graph modeling, and hypothesis testing theory—requiring only partial network observations. Experiments on synthetic and real-world contact networks demonstrate that the proposed method significantly improves the representational accuracy of minority groups in top-ranked positions (average gain of 32%), while preserving overall ranking quality. The core contribution is a testable and correctable theoretical and algorithmic foundation for structural fairness in graph learning, bridging fairness-aware inference with incomplete network data.

This paper addresses the challenge of quantifying homophily—i.e., the tendency of similar nodes to co-occur in group interactions—in hypergraphs. Methodologically, it introduces the first hyperedge-centric homophily analysis framework grounded in perplexity: it defines *interaction perplexity* to measure attribute diversity within hyperedges and constructs a degree-preserving randomized baseline; homophily is then quantified via a normalized “diversity gap,” yielding a global *Perplexity-Homophily* index. Its key contribution lies in pioneering the use of perplexity for hypergraph homophily modeling, enabling sensitive detection of dynamic homophilous or heterophilous tendencies across hyperedges of varying sizes. Experiments on synthetic and real-world hypergraphs demonstrate that the proposed index accurately characterizes homophily distribution patterns and size-dependent trends, significantly outperforming existing pairwise-relation-based metrics.

Existing research on fairness in graph link prediction has largely focused on homophily bias, overlooking broader topological biases and thereby limiting the generalizability of fairness interventions. This work proposes the first benchmark framework for fair link prediction that systematically incorporates non-homophilous topological biases. The framework formalizes a taxonomy of topological biases, introduces a controllable graph generation mechanism to instantiate diverse structural settings, and comprehensively evaluates both classical and fairness-aware models across varied topologies. Experimental results reveal that current methods are highly sensitive to non-homophilous structural biases, highlighting a critical gap in existing approaches. By establishing a new paradigm for structure-aware fairness evaluation in graph learning, this study provides both empirical insights and methodological foundations for future research in equitable graph representation learning.

Existing hypergraph clustering coefficients treat hyperedges as atomic units, ignoring pairwise interactions among their constituent nodes—leading to spurious zero values for nodes embedded in nontrivial clustering structures. Method: We propose a novel hypergraph clustering coefficient that explicitly models intra-hyperedge pairwise relational strength via a mapping from hypergraphs to weighted graphs. Contribution/Results: The proposed coefficient rigorously satisfies three theoretical desiderata: (i) boundedness in [0,1], (ii) consistency with the classical graph clustering coefficient upon graph degeneration, and (iii) faithful characterization of higher-order local structure. Validated through higher-order motif analysis and real-world social and collaboration datasets, it significantly corrects the zero-value bias of conventional methods on 3-node motifs (III, IV-a, IV-b) and provides finer-grained, more accurate quantification of local density—especially for large hyperedges.

This study addresses the challenge of characterizing and quantifying higher-order homophily and heterophily in hypergraphs by proposing the first unified framework that integrates both measurement and generative modeling. Clarifying the conceptual distinctions between higher-order mixing patterns and traditional pairwise homophily, the work establishes a comprehensive suite of metrics tailored specifically for hypergraphs. It further provides a systematic review of existing random hypergraph generative models, delineating the conditions under which each model family is appropriate. By laying a coherent theoretical foundation for the study of higher-order homophily, this research offers clear methodological guidance for future model selection and design, thereby advancing the broader field of higher-order network analysis.

Existing graph centrality measures lack a unified, quantifiable framework for systematic comparison, hindering the formalization and validation of related conjectures. This work proposes a mathematical approach based on vertex rankings to construct the first computable approximation framework capable of systematically comparing any two centrality measures. By integrating graph theory, formal modeling, and approximation algorithms, the method not only verifies several classical conjectures but also generates novel hypotheses of independent research interest. The framework thus establishes a theoretical foundation for network science and opens new avenues for future investigation.

This work addresses the overlooked issue of fairness disparities among sensitive attribute groups in multi-hop graph structures when promoting inter-group connections for link prediction. The paper introduces the concept of k-hop fairness and, for the first time, formalizes a structural bias metric that accounts for multi-hop distances, thereby revealing the intrinsic dependence between fairness and graph topology. This approach transcends the limitations of conventional methods that focus solely on first-order neighborhoods or pairwise fairness. By designing preprocessing and postprocessing strategies based on graph rewiring, the proposed method effectively mitigates multi-hop structural bias on standard benchmarks. Experimental results demonstrate that the approach significantly outperforms existing baselines in terms of multi-hop fairness while maintaining competitive link prediction performance.

This study addresses the lack of effective metrics for individual fairness in existing community detection methods, which may lead to similar nodes being assigned to different communities in an unfair manner. The authors propose a novel vector distance measure derived from the community co-occurrence matrix, enabling, for the first time, a computable quantification of individual fairness. They systematically evaluate the fairness–performance trade-offs of several algorithms—including Significance, Surprise, Combo, Leiden, and SBMDL—on both synthetic and real-world networks. Their analysis reveals that individual and group fairness are not interchangeable and are significantly influenced by the detectability of community structure. Notably, high group fairness or clustering accuracy does not guarantee individual fairness. The study further identifies algorithms that achieve superior fairness–quality trade-offs in dense versus sparse graphs.

This study addresses the limitations of traditional node similarity measures, which often assume a uniform and continuous feature space and thus fail to capture the true structural equivalence among nodes in attributed networks. By integrating neighborhood attribute profiling, dimensionality reduction, and visualization techniques, the authors uncover complex nonlinear manifold structures and density biases inherent in high-dimensional feature spaces. Empirical analysis on an enterprise transaction network reveals that semantically identical industry labels can correspond to multiple disconnected regions of structural roles, and that supply chain tiers exhibit continuous transitions rather than discrete partitions. These findings motivate the proposal of a new similarity metric grounded in manifold topology to more accurately reflect structural equivalence among nodes.