Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.06534

Vertex-subgraph eigenvector centrality for connected induced subgraphs

Qingying Zhang·Haotian Zeng·Changjiang Bu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Eigenvector centrality evaluates the importance of vertices through adjacency relations, while higher-order subgraph structures provide additional information for centrality analysis. This motivates the simultaneous evaluation of vertices and subgraphs within a unified spectral framework. In this paper, we propose vertex-subgraph eigenvector centrality (VSC), which jointly determines the centralities of vertices and connected induced subgraphs of order three. The vertex centrality depends on the centralities of the subgraphs containing it and those of the other vertices in these subgraphs, whereas the subgraph centrality depends on the centralities of its constituent vertices. To distinguish induced paths P3 from triangles K3, the capacity of each subgraph is defined as its number of edges. The resulting coupled nonlinear eigenvalue equations are represented by a fourth-order symmetric nonnegative tensor. We prove that this tensor is weakly irreducible for every connected graph with at least three vertices, which guarantees the existence and uniqueness, up to scaling, of a positive Perron eigenvector. Numerical experiments on four real-world networks compare VSC with classical centrality measures and show that capacity weighting has a greater effect on subgraph rankings than on vertex rankings.

Explore related subjects

cs.SI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Qingying Zhang, Haotian Zeng, Changjiang Bu. 2026-11-04. Vertex-subgraph eigenvector centrality for connected induced subgraphs. https://arxiv.org/abs/2611.06534

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

No Note Is an Island: Probing LLMs' Understanding of Crowdsourced Fact-Checking Environments

Large language models (LLMs) increasingly assist crowdsourced fact-checking, yet evaluations focus on individual annotations. A correction's reach and reception depend on visibility, audience responses, and platform policies. We introduce correction context understanding: assessing corrective content, interpreting audience responses, and reasoning about platform dynamics within a shared environment. We build NoteHabitat from 36 months of Weibo Annotations data, linking 102,994 posts (42,853 annotations), 431,407 comments, and five policy events. Evaluating diverse model families across seven tasks spanning content, interaction, and management reveals three gaps. Annotation quality correlates only weakly with engagement ($ρ=0.068$), while four zero-shot LLMs systematically underrate quality relative to human judgments, especially evidence support and objectivity. Models also miss toxic comments supporting corrections (36.4% average recall across ten models). At the platform level, LLMs partially predict policy-associated outcome directions, but LLM-guided simulations poorly reproduce daily activity. Cross-group analyses expose blind spots tied to contribution types and reader stances that aggregate scores conceal. Reliable fact-checking AI must understand the note, the conversation around it, and the platform in which both unfold.

cs.SI↗
arXiv2026

Adjustment-Anchor Dependence in Formulaic Alpha Languages: A Certified Grammar and a Re-Anchoring Audit

Several public scripts for formulaic alpha mining store prices adjusted to the snapshot's last day, so a past day's stored price changes with every later split or dividend and formulas that do not cancel the adjustment factor depend on future corporate actions. We formalise a change of adjustment anchor as a per-stock group action and give a two-sorted type system that soundly certifies anchor invariance from a formula's syntax, under a declared field-adjustment contract and idealised operator semantics; its second sort admits log-returns, and a linear-time checker plugs into any miner. In a re-anchoring audit on Chinese A-shares, pools that five published methods mined in our benchmark pipeline score a mean information coefficient (IC) 0.005 higher on the stored representation than on a cutoff-anchored one, about 14% of their IC. Certified pools move by 0.001 or less, and pools mined on past-anchored data stay sensitive. On the Chinese development folds, certification shows no detectable predictive cost or gain at the design's resolution, about 0.017 IC across cells on pool ICs of 0.03-0.04. We also trace an erroneous index-membership entry to public Qlib data snapshots and show that re-mining exposes the effect of such data defects, which re-evaluating fixed pools misses.

cs.SI↗
arXiv2026

CasHyper: Modeling Multi-Factor Interactions and Asymmetric Influence in Cascade Prediction via Hypercomplex Algebra

Cascade prediction aims to forecast the future evolution of information diffusion and is an important task in social network analysis. Most existing methods represent users and cascades in real-valued Euclidean spaces, which may offer limited capacity to model multi-factor interactions and asymmetric influence in complex diffusion processes. To address these challenges, we propose CasHyper, a hypercomplex-based cascade prediction framework that integrates hypercomplex algebra with graph neural networks and Transformers. CasHyper organizes user and cascade embeddings into multiple hypercomplex components, with each component encoding distinct latent factors, and uses structured algebraic operations to model cross-component interactions. The non-commutative hypercomplex product further yields order-dependent interaction representations, enabling the model to learn asymmetric influence among users. In the network encoding stage, a static heterogeneous graph channel captures user-user and user-cascade relations, while a Neural ODE-based dynamic channel models the continuous evolution of node states and edge weights. A hypercomplex Transformer with norm-preserving rotary transformations is then introduced to incorporate relative positional information into cascade sequence modeling. Finally, an interaction-aware module and a linear projection module are combined to estimate the probability of each candidate user participating next. Experiments on four real-world datasets show that CasHyper achieves competitive or better performance than the compared methods under the evaluated settings, including relative improvements of up to $43.24\%$ on Android and $18.43\%$ on Christianity in Hits@50.

cs.SI↗