Tootfinder

Now out in #TMLR:
🍇 GRAPES: Learning to Sample Graphs for Scalable Graph Neural Networks 🍇
There's lots of work on sampling subgraphs for GNNs, but relatively little on making this sampling process _adaptive_. That is, learning to select the data from the graph that is relevant for your task.
We introduce an RL-based and a GFLowNet-based sampler and show that the approach perf…

Efficient Semi-External Breadth-First Search
Xiaolong Wan, Xixian Han
https://arxiv.org/abs/2507.12925 https://arxiv.org/pdf/2507.129…

Efficient Semi-External Breadth-First Search
Breadth-first search (BFS) is known as a basic search strategy for learning graph properties. As the scales of graph databases have increased tremendously in recent years, large-scale graphs G are often disk-resident. Obtaining the BFS results of G in semi-external memory model is inevitable, because the in-memory BFS algorithm has to maintain the entire G in the main memory, and external BFS algorithms consume high computational costs. As a good trade-off between the internal and external memo…

Explain First, Trust Later: LLM-Augmented Explanations for Graph-Based Crypto Anomaly Detection
Adriana Watson
https://arxiv.org/abs/2506.14933 https://

Explain First, Trust Later: LLM-Augmented Explanations for Graph-Based Crypto Anomaly Detection
The decentralized finance (DeFi) community has grown rapidly in recent years, pushed forward by cryptocurrency enthusiasts interested in the vast untapped potential of new markets. The surge in popularity of cryptocurrency has ushered in a new era of financial crime. Unfortunately, the novelty of the technology makes the task of catching and prosecuting offenders particularly challenging. Thus, it is necessary to implement automated detection tools related to policies to address the growing cri…

Scene Graph-Guided Proactive Replanning for Failure-Resilient Embodied Agent
Che Rin Yu, Daewon Chae, Dabin Seo, Sangwon Lee, Hyeongwoo Im, Jinkyu Kim
https://arxiv.org/abs/2508.11286

Scene Graph-Guided Proactive Replanning for Failure-Resilient Embodied Agent
When humans perform everyday tasks, we naturally adjust our actions based on the current state of the environment. For instance, if we intend to put something into a drawer but notice it is closed, we open it first. However, many autonomous robots lack this adaptive awareness. They often follow pre-planned actions that may overlook subtle yet critical changes in the scene, which can result in actions being executed under outdated assumptions and eventual failure. While replanning is critical fo…

Parallel Complexity of Depth-First-Search and Maximal path
Archit Chauhan, Samir Datta, M. Praveen
https://arxiv.org/abs/2506.14974 https://

Parallel Complexity of Depth-First-Search and Maximal path
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deter…

Short monochromatic odd cycles
Oliver Janzer, Fredy Yip
https://arxiv.org/abs/2506.14910 https://arxiv.org/pdf/2506.14910

Short monochromatic odd cycles
It is easy to see that every $k$-edge-colouring of the complete graph on $2^k+1$ vertices contains a monochromatic odd cycle. In 1973, Erdős and Graham asked to estimate the smallest $L(k)$ such that every $k$-edge-colouring of $K_{2^k+1}$ contains a monochromatic odd cycle of length at most $L(k)$. Recently, Girão and Hunter obtained the first nontrivial upper bound by showing that $L(k)=O(\frac{2^k}{k^{1-o(1)}})$, which improves the trivial bound by a polynomial factor. We obtain an exponen…

Congested Clique Counting for Local Gibbs Distributions
Joshua Z. Sobel
https://arxiv.org/abs/2508.13083 https://arxiv.org/pdf/2508.13083

Congested Clique Counting for Local Gibbs Distributions
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we demonstrate the first approximate counting algorithm in the CongestedClique for a wide range of problems. Most interestingly, we present an algorithm for approximating the number of $q$-colorings of a graph within $ε$-multiplicative error, when $q>αΔ$ for any…

Factor Graph Optimization for Leak Localization in Water Distribution Networks
Paul Irofti, Luis Romero-Ben, Florin Stoican, Vicen\c{c} Puig
https://arxiv.org/abs/2509.10982 htt…

Factor Graph Optimization for Leak Localization in Water Distribution Networks
Detecting and localizing leaks in water distribution network systems is an important topic with direct environmental, economic, and social impact. Our paper is the first to explore the use of factor graph optimization techniques for leak localization in water distribution networks, enabling us to perform sensor fusion between pressure and demand sensor readings and to estimate the network's temporal and structural state evolution across all network nodes. The methodology introduces specific wat…

Codes on any Cayley Graph have an Interactive Oracle Proof of Proximity
Hugo Delavenne (GRACE), Louise Lallemand (GRACE)
https://arxiv.org/abs/2508.10510 https://

Codes on any Cayley Graph have an Interactive Oracle Proof of Proximity
Interactive Oracle Proofs of Proximity (IOPP) are at the heart of code-based SNARKs, a family of zeroknowledge protocols. The first and most famous one is the FRI protocol [BBHR18a], that efficiently tests proximity to Reed-Solomon codes. This paper generalizes the flowering IOPP introduced in [DMR25] for some specific (2, n)-regular Tanner codes to a much broader variety of codes: any code with symbols indexed on the edges of a Cayley graph. The flowering protocol of [DMR25] had a soundness pa…

Solar continues to surge
In keeping with China’s green push, the country is leading the surge in global solar installations. In the first half of 2025, the world installed 380 GW of new solar capacity, a 64% jump from the same period last year. China accounted for 67% of that growth, installing more than twice the rest of the world combined.

A Machine Learning Framework for Modeling Ensemble Properties of Atomically Disordered Materials
Zhenyao Fang, Ting-Wei Hsu, Qimin Yan
https://arxiv.org/abs/2506.15652

A Machine Learning Framework for Modeling Ensemble Properties of Atomically Disordered Materials
Disorder, though naturally present in experimental samples and strongly influencing a wide range of material phenomena, remains underexplored in first-principles studies due to the computational cost of sampling the large supercell and configurational space. The recent development of machine learning techniques, particularly graph neural networks (GNNs), has enabled the efficient and accurate predictions of complex material properties, offering promising tools for studying disordered systems. I…

Hyper-Zagreb Indices of Hypergraphs with Application in Drug Design
Abdulkafi Sanad
https://arxiv.org/abs/2509.13787 https://arxiv.org/pdf/2509.13787

Hyper-Zagreb Indices of Hypergraphs with Application in Drug Design
Let $\mathcal{H}$ be a hypergraph on the non-empty finite vertex set $V(\mathcal{H})$ with the hyperedge set $E(\mathcal{H})$, where each hyperedge $e \in E(\mathcal{H})$ is a subset of $V(\mathcal{H})$ with at least two vertices. This paper introduces the first and second Hyper-Zagreb indices for hypergraphs, extending these well-known graph indices to hypergraphs. We discuss bounds on these indices for general hypergraphs, weak bipartite hypergraphs, hypertrees, $k$-uniform hypergraphs, $k$-u…

SPARK: Adaptive Low-Rank Knowledge Graph Modeling in Hybrid Geometric Spaces for Recommendation
Binhao Wang, Yutian Xiao, Maolin Wang, Zhiqi Li, Tianshuo Wei, Ruocheng Guo, Xiangyu Zhao
https://arxiv.org/abs/2509.11094

SPARK: Adaptive Low-Rank Knowledge Graph Modeling in Hybrid Geometric Spaces for Recommendation
Knowledge Graphs (KGs) enhance recommender systems but face challenges from inherent noise, sparsity, and Euclidean geometry's inadequacy for complex relational structures, critically impairing representation learning, especially for long-tail entities. Existing methods also often lack adaptive multi-source signal fusion tailored to item popularity. This paper introduces SPARK, a novel multi-stage framework systematically tackling these issues. SPARK first employs Tucker low-rank decomposition …

Robust Multi-Manifold Clustering via Simplex Paths
Haoyu Chen, Anna Little, Akin Narayan
https://arxiv.org/abs/2507.10710 https://arx…

Robust Multi-Manifold Clustering via Simplex Paths
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the graph weights, and then compute infinity path distances in this simplex graph. This procedure gives a metric on simplices which we refer to as the largest angle path dista…

Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants
Leonhard Nagel
https://arxiv.org/abs/2507.12502

Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants
We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \geq 3$ and deterministic unit vector $\mathbf{q} \perp \mathbf{e}$, we prove that the normalized overlap $\sqrt{N}\langle \mathbf{q}, \mathbf{u}_2 \rangle$ satisfies \[ \sup_{x \in \mathbb{R}} \left|\mathbb{P}\left(\sqrt{N}\langle \mathbf{q}, \mathbf{u}_2 \rangle \leq x\right) - Φ(x)\right| \leq C_d N^{-1/6+\varepsi…

Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation
Anjie Qiao, Zhen Wang, Chuan Chen, DeFu Lian, Enhong Chen
https://arxiv.org/abs/2509.09451

Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation
Controllable molecular graph generation is essential for material and drug discovery, where generated molecules must satisfy diverse property constraints. While recent advances in graph diffusion models have improved generation quality, their effectiveness in multi-conditional settings remains limited due to reliance on joint conditioning or continuous relaxations that compromise fidelity. To address these limitations, we propose Composable Score-based Graph Diffusion model (CSGD), the first mo…

Electrification is still marginal in the Netherlands. Dutch electricity consumption in the first half of 2025 was almost exactly the same as a decade ago, in the first half of 2015 ( 0.3%).
Efficiency gains compensated for the modest shares of electric cars and heat pumps that did enter the scene.
Source:

Meer elektriciteit uit fossiele bronnen
Nederland produceerde in het eerste halfjaar van 2025 64 miljard kWh elektriciteit. Dit is 7 procent meer dan in het eerste halfjaar van 2024. Met name de productie uit fossiele bronnen steeg, vooral uit kolen. De productie uit hernieuwbare bronnen was lager, vooral uit windenergie. De productie uit zonne-energie piekte in het tweede kwartaal. Het verbruik van elektriciteit bleef gelijk. Dit meldt het Centraal Bureau voor de Statistiek (CBS) op basis van voorlopige cijfers.

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

RAGulating Compliance: A Multi-Agent Knowledge Graph for Regulatory QA
Bhavik Agarwal, Hemant Sunil Jomraj, Simone Kaplunov, Jack Krolick, Viktoria Rojkova
https://arxiv.org/abs/2508.09893

RAGulating Compliance: A Multi-Agent Knowledge Graph for Regulatory QA
Regulatory compliance question answering (QA) requires precise, verifiable information, and domain-specific expertise, posing challenges for Large Language Models (LLMs). In this work, we present a novel multi-agent framework that integrates a Knowledge Graph (KG) of Regulatory triplets with Retrieval-Augmented Generation (RAG) to address these demands. First, agents build and maintain an ontology-free KG by extracting subject--predicate--object (SPO) triplets from regulatory documents and syst…

Exact Tur\'{a}n number of the Fano plane in the $\ell_2$-norm
Jianfeng Hou, Xizhi Liu, Yixiao Zhang
https://arxiv.org/abs/2507.12354 https://

Exact Turán number of the Fano plane in the $\ell_2$-norm
A classical object in hypergraph Turán theory is the Fano plane $\mathbb{F}$, the unique linear $3$-graph on seven vertices with seven edges. The Turán density and exact Turán number of $\mathbb{F}$, first proposed as a problem by Sós~\cite{Sos76} in the 1970s, were determined through a sequence of works by De Caen--Füredi \cite{DCF00}, Füredi-Simonovits \cite{FS05}, Keevash-Sudakov \cite{KS05}, and Bellmann-Reiher \cite{BR19}. Addressing a conjecture of Balogh--Clemen--Lidický \cite[C…

Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems
Evan Sundbo
https://arxiv.org/abs/2509.12368 https://arxiv.org/pdf/25…

Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems
In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincaré polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincar…

RJD-BASE: Multi-Modal Spectral Clustering via Randomized Joint Diagonalization
Haoze He, Artemis Pados, Daniel Kressner
https://arxiv.org/abs/2509.11981 https://

RJD-BASE: Multi-Modal Spectral Clustering via Randomized Joint Diagonalization
We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonalization, spectral co-regularization, and multiview clustering--attempt to align embeddings across modalities, they often rely on costly iterative refinement and may fail to directly target the spectral subspace relevant for clustering. In this work, we introduce two key innovations. First, we bring the power of random…

The Directed Spanning Forest: coalescence versus dimension
Tom Garcia-Sanchez
https://arxiv.org/abs/2507.13289 https://arxiv.org/pdf/…

The Directed Spanning Forest: coalescence versus dimension
For $p\in[1,\infty]$, the $\ell^p$ directed spanning forest (DSF) of dimension $d\geq 2$ is an oriented random geometric graph whose vertex set is given by a homogeneous Poisson point process $\mathcal N$ on $\mathbb R^d$ and whose edges consist of all pairs $(x, y)\in\mathcal N^2$ such that $y$ is the closest point to $x$ in $\mathcal N$ for the $\ell^p$ distance among points with a strictly larger $e_d$ coordinate. First introduced by Baccelli and Bordenave in 2007 in the case $p=d=2$, this g…

Sublinear Morse Geodesics and First Passage Percolation
Sagnik Jana, Yulan Qing
https://arxiv.org/abs/2507.07859 https://arxiv.org/pd…

Sublinear Morse Geodesics and First Passage Percolation
Given an infinite connected graph, a way to randomly perturb its metric is to assign random i.i.d. lengths to the edges of the graph. Assume that the graph is infinite and of bounded degree. Assume also strict positivity and finite expectation of the edge length distribution and existence of a sublinearly Morse bi-infinite geodesic line, we prove that almost surely there exists a bi-infinite geodesic line. This generalizes a previous result of \cite{BT17} regarding Morse geodesics.

Mixed Discrete and Continuous Planning using Shortest Walks in Graphs of Convex Sets
Savva Morozov, Tobia Marcucci, Bernhard Paus Graesdal, Alexandre Amice, Pablo A. Parrilo, Russ Tedrake
https://arxiv.org/abs/2507.10878

Mixed Discrete and Continuous Planning using Shortest Walks in Graphs of Convex Sets
We study the Shortest-Walk Problem (SWP) in a Graph of Convex Sets (GCS). A GCS is a graph where each vertex is paired with a convex program, and each edge couples adjacent programs via additional costs and constraints. A walk in a GCS is a sequence of vertices connected by edges, where vertices may be repeated. The length of a walk is given by the cumulative optimal value of the corresponding convex programs. To solve the SWP in GCS, we first synthesize a piecewise-quadratic lower bound on the…

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

GeoLayer: Towards Low-Latency and Cost-Efficient Geo-Distributed Graph Stores with Layered Graph
Feng Yao, Xiaokang Yang, Shufeng Gong, Song Yu, Yanfeng Zhang, Ge Yu
https://arxiv.org/abs/2509.02106

GeoLayer: Towards Low-Latency and Cost-Efficient Geo-Distributed Graph Stores with Layered Graph
The inherent connectivity and dependency of graph-structured data, combined with its unique topology-driven access patterns, pose fundamental challenges to conventional data replication and request routing strategies in geo-distributed cloud storage systems. In this paper, we propose GeoLayer, a geo-distributed graph storage framework that jointly optimizes graph replica placement and pattern request routing. We first construct a latency-aware layered graph architecture that decomposes the grap…

Lower bounds for dominating set reconfiguration on sparse (directed) graphs
Jona Dirks, Alexandre Vigny
https://arxiv.org/abs/2507.11446 https://

Lower bounds for dominating set reconfiguration on sparse (directed) graphs
In a graph, a vertex dominates itself and its neighbors, and a dominating set is a set of vertices that together dominate the entire graph. Given a graph and two dominating sets of equal size $k$, the {\em Dominating Set Reconfiguration with Token sliding} (DSR-TS) problem asks whether one can, by iteratively replacing a vertex by an adjacent one, transform the first set into the second one, while ensuring that every set during the reconfiguration process is a dominating set. The token jumpin…

Fast Percolation Centrality Approximation with Importance Sampling
Antonio Cruciani, Leonardo Pellegrina
https://arxiv.org/abs/2509.11454 https://arxiv.org…

Fast Percolation Centrality Approximation with Importance Sampling
In this work we present PercIS, an algorithm based on Importance Sampling to approximate the percolation centrality of all the nodes of a graph. Percolation centrality is a generalization of betweenness centrality to attributed graphs, and is a useful measure to quantify the importance of the vertices in a contagious process or to diffuse information. However, it is impractical to compute it exactly on modern-sized networks. First, we highlight key limitations of state-of-the-art sampling-bas…

Evaluating Efficiency and Novelty of LLM-Generated Code for Graph Analysis
Atieh Barati Nia, Mohammad Dindoost, David A. Bader
https://arxiv.org/abs/2507.06463

Evaluating Efficiency and Novelty of LLM-Generated Code for Graph Analysis
Large Language Models (LLMs) are increasingly used to automate software development, yet most prior evaluations focus on functional correctness or high-level languages such as Python. We present the first systematic study of LLMs' ability to generate efficient C implementations of graph-analysis routines--code that must satisfy the stringent runtime and memory constraints. Eight state-of-the-art models (OpenAI ChatGPT o3 and o4-mini-high, Anthropic Claude 4 Sonnet and Sonnet Extended, Google Ge…

Tight complexity bounds for diagram commutativity verification
Artem Malko, Igor Spiridonov
https://arxiv.org/abs/2509.11331 https://arxiv.org/pdf/2509.113…

Tight complexity bounds for diagram commutativity verification
A diagram $\mathcal{D} = (G, l)$ over a monoid $M$ is an oriented graph $G = (V, E)$ endowed with a labeling $l\colon E \to M$. A diagram is commutative if and only if for any two oriented paths with the same endpoints, the products in $M$ of their edge labels coincide. We propose the first asymptotically optimal algorithm for diagram commutativity verification applicable to all graph families. For graphs with $\lvert V\rvert \preceq \lvert E\rvert \preceq \lvert V\rvert^2$, which covers most p…

Self-adjoint extensions for the Laplacian operator on non-compacts graphs and the existence and stability of standing waves for NLS models
Jaime Angulo Pava, Alexander Munoz
https://arxiv.org/abs/2507.10821

Self-adjoint extensions for the Laplacian operator on non-compacts graphs and the existence and stability of standing waves for NLS models
In this work we first study a systematic way to describe the unitary dynamics of the Schrödinger operator on a looping-edge graphs $\mathcal{G}$ (a graph consisting of a circle and a finite amount $N$ of infinite half-lines attached to a common vertex). We also apply our approach on $\mathcal T$-shaped graphs (metric graphs that consists of a pendant edge and a finite amount of half-lines attached to the common vertex). In both cases we obtain novel boundary conditions on the unique vertex tha…

Context Pooling: Query-specific Graph Pooling for Generic Inductive Link Prediction in Knowledge Graphs
Zhixiang Su, Di Wang, Chunyan Miao
https://arxiv.org/abs/2507.07595

Context Pooling: Query-specific Graph Pooling for Generic Inductive Link Prediction in Knowledge Graphs
Recent investigations on the effectiveness of Graph Neural Network (GNN)-based models for link prediction in Knowledge Graphs (KGs) show that vanilla aggregation does not significantly impact the model performance. In this paper, we introduce a novel method, named Context Pooling, to enhance GNN-based models' efficacy for link predictions in KGs. To our best of knowledge, Context Pooling is the first methodology that applies graph pooling in KGs. Additionally, Context Pooling is first-of-its-ki…

Triangle-Covered Graphs: Algorithms, Complexity, and Structure
Amirali Madani, Anil Maheshwari, Babak Miraftab, Pawe{\l} \.Zyli\'nski
https://arxiv.org/abs/2509.11448 https:…

Triangle-Covered Graphs: Algorithms, Complexity, and Structure
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into a triangle-covered graph (one in which every vertex belongs to at least one triangle). We first present tight lower bounds on the number of edges in any connected triangle-covered graph of order $n$, and then we characterize all connected graphs that attain …

Developing and evaluating quilts for the depiction of large layered graphs
Juhee Bae, Benjamin Watson
https://arxiv.org/abs/2507.10883 https://

Developing and evaluating quilts for the depiction of large layered graphs
Traditional layered graph depictions such as flow charts are in wide use. Yet as graphs grow more complex, these depictions can become difficult to understand. Quilts are matrix-based depictions for layered graphs designed to address this problem. In this research, we first improve Quilts by developing three design alternatives, and then compare the best of these alternatives to better-known node-link and matrix depictions. A primary weakness in Quilts is their depiction of skip links, links th…

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
Futian Wang, Yuhan Qiao, Xiao Wang, Fuling Wang, Yuxiang Zhang, Dengdi Sun
https://arxiv.org/abs/2508.03426

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
X-ray medical report generation is one of the important applications of artificial intelligence in healthcare. With the support of large foundation models, the quality of medical report generation has significantly improved. However, challenges such as hallucination and weak disease diagnostic capability still persist. In this paper, we first construct a large-scale multi-modal medical knowledge graph (termed M3KG) based on the ground truth medical report using the GPT-4o. It contains 2477 enti…

TLV-HGNN: Thinking Like a Vertex for Memory-efficient HGNN Inference
Dengke Han, Duo Wang, Mingyu Yan, Xiaochun Ye, Dongrui Fan
https://arxiv.org/abs/2508.07796 https://

TLV-HGNN: Thinking Like a Vertex for Memory-efficient HGNN Inference
Heterogeneous graph neural networks (HGNNs) excel at processing heterogeneous graph data and are widely applied in critical domains. In HGNN inference, the neighbor aggregation stage is the primary performance determinant, yet it suffers from two major sources of memory inefficiency. First, the commonly adopted per-semantic execution paradigm stores intermediate aggregation results for each semantic prior to semantic fusion, causing substantial memory expansion. Second, the aggregation process …

Attributed-graphs kernel implementation using local detuning of neutral-atoms Rydberg Hamiltonian
Mehdi Djellabi, Matthias Hecker, Shaheen Acheche
https://arxiv.org/abs/2509.09421

Attributed-graphs kernel implementation using local detuning of neutral-atoms Rydberg Hamiltonian
We extend the quantum-feature kernel framework, which relies on measurements of graph-dependent observables, along three directions. First, leveraging neutral-atom quantum processing units (QPUs), we introduce a scheme that incorporates attributed graphs by embedding edge features into atomic positions and node features into local detuning fields of a Rydberg Hamiltonian. We demonstrate both theoretically and empirically that local detuning enhances kernel expressiveness. Second, in addition to…

Adversarial Attacks and Defenses on Graph-aware Large Language Models (LLMs)
Iyiola E. Olatunji, Franziska Boenisch, Jing Xu, Adam Dziedzic
https://arxiv.org/abs/2508.04894 http…

Adversarial Attacks and Defenses on Graph-aware Large Language Models (LLMs)
Large Language Models (LLMs) are increasingly integrated with graph-structured data for tasks like node classification, a domain traditionally dominated by Graph Neural Networks (GNNs). While this integration leverages rich relational information to improve task performance, their robustness against adversarial attacks remains unexplored. We take the first step to explore the vulnerabilities of graph-aware LLMs by leveraging existing adversarial attack methods tailored for graph-based models, i…

Counting Graph Homomorphisms in Bipartite Settings
Igal Sason
https://arxiv.org/abs/2508.06977 https://arxiv.org/pdf/2508.06977

Counting Graph Homomorphisms in Bipartite Settings
This paper studies the problem of counting homomorphisms from a bipartite source graph to a bipartite target graph. An exact formula is first derived for the number of homomorphisms from a complete bipartite graph into a general bipartite graph. While exact, this formula is typically computationally intensive to evaluate. To address this, computable combinatorial lower bounds are established. When the target graph contains no 4-cycles, the lower bound simplifies and becomes exact. Two additiona…

Augmentation Algorithms for Total Variation-Regularized Integer Programs
Dominic Yang, Sven Leyffer, Miles Bakenhus
https://arxiv.org/abs/2508.05822 https://

Augmentation Algorithms for Total Variation-Regularized Integer Programs
We address a class of integer optimization programs with a total variation-like regularizer and convex, separable constraints on a graph. Our approach makes use of the Graver basis, an optimality certificate for integer programs, which we characterize as corresponding to the collection of induced connected subgraphs of our graph. We demonstrate how to use this basis to craft an exact global optimization algorithm for the unconstrained problem recovering a method first shown in [16]. We then pre…

MX-AI: Agentic Observability and Control Platform for Open and AI-RAN
Ilias Chatzistefanidis, Andrea Leone, Ali Yaghoubian, Mikel Irazabal, Sehad Nassim, Lina Bariah, Merouane Debbah, Navid Nikaein
https://arxiv.org/abs/2508.09197

MX-AI: Agentic Observability and Control Platform for Open and AI-RAN
Future 6G radio access networks (RANs) will be artificial intelligence (AI)-native: observed, reasoned about, and re-configured by autonomous agents cooperating across the cloud-edge continuum. We introduce MX-AI, the first end-to-end agentic system that (i) instruments a live 5G Open RAN testbed based on OpenAirInterface (OAI) and FlexRIC, (ii) deploys a graph of Large-Language-Model (LLM)-powered agents inside the Service Management and Orchestration (SMO) layer, and (iii) exposes both observ…

Data collected by Mauna Loa from 1958 onward let us clearly see the evidence of climate change for the first time.
The station samples the air and measures global CO₂ levels.
Charles Keeling and his successors used this data to produce the famous Keeling curve – a graph showing carbon dioxide levels increasing year after year.
But this precious record is in peril.
Donald Trump has decided to defund the observatory recording the data -- as well as the widespread US gre…

Mauna Loa Observatory captured the reality of climate change. The US plans to shut it down
Cutting data climate collection – as the Trump administration is now trying to do – is like breaking a thermometer to avoid knowing you’ve got a fever.

W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
Daniel Drimbe, Stefaan Vaes
https://arxiv.org/abs/2507.04691 https://

W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II$_1$ factors. As a consequence, we construct the first uncountable family of discrete groups $Γ$ that are not von Neumann equivalent, which means that their group von Neumann algebras $L(Γ)$ are not W*-correlated, and wh…

Deterministic Lower Bounds for $k$-Edge Connectivity in the Distributed Sketching Model
Peter Robinson, Ming Ming Tan
https://arxiv.org/abs/2507.11257 http…

Deterministic Lower Bounds for $k$-Edge Connectivity in the Distributed Sketching Model
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the referee must decide whether the graph is $k$-edge connected by taking into account the received messages. We present the first lower bound for deciding a graph connectivity problem in this model with a deterministic algorithm. Concretely, we show that the …

So now I have unroutable messages in #RabbitMQ for the first time ever, and other weird as #fuck other network glitches. Like the spike in the graph only showing up after 40 seconds instead of right away. Often

IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing
Shusen Ma, Tianhao Zhang, Qijiu Xia, Yun-Bo Zhao
https://arxiv.org/abs/2509.07725

IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing
Multivariate time series forecasting (MTSF) often faces challenges from missing variables, which hinder conventional spatial-temporal graph neural networks in modeling inter-variable correlations. While GinAR addresses variable missing using attention-based imputation and adaptive graph learning for the first time, it lacks interpretability and fails to capture more latent temporal patterns due to its simple recursive units (RUs). To overcome these limitations, we propose the Interpretable Bidi…

A new take on district heating and #flexibility: can dynamic pricing help reduce overall heating costs? The short answer is yes, and automatic controllers would reinforce this effect. Peak heat demand, sometimes also from fossil sources, can thus be reduced.

Big News! The completely #opensource #LLM #Apertus 🇨🇭 has been released today:
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Apertus: A fully open, transparent, multilingual language model
EPFL, ETH Zurich and the Swiss National Supercomputing Centre (CSCS) released Apertus today, Switzerland’s first large-scale, open, multilingual language model — a milestone in generative AI for transparency and diversity.

CROP: Integrating Topological and Spatial Structures via Cross-View Prefixes for Molecular LLMs
Jianting Tang, Yubo Wang, Haoyu Cao, Linli Xu
https://arxiv.org/abs/2508.06917 ht…

CROP: Integrating Topological and Spatial Structures via Cross-View Prefixes for Molecular LLMs
Recent advances in molecular science have been propelled significantly by large language models (LLMs). However, their effectiveness is limited when relying solely on molecular sequences, which fail to capture the complex structures of molecules. Beyond sequence representation, molecules exhibit two complementary structural views: the first focuses on the topological relationships between atoms, as exemplified by the graph view; and the second emphasizes the spatial configuration of molecules, …

Bespoke multiresolution analysis of graph signals
Giacomo Elefante, Gianluca Giacchi, Michael Multerer, Jacopo Quizi
https://arxiv.org/abs/2507.19181 https://

Bespoke multiresolution analysis of graph signals
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the analysis of scattered data. The first contribution of this work is defining samplets on graphs. To this end, we subdivide the graph into a fixed number of patches, embed each patch into a Euclidean space, where we construct samplets, and eventually pull the co…

Free modules of splines on edge-labeled graphs over $k[x,y]$
Kyle Stoltz
https://arxiv.org/abs/2509.05840 https://arxiv.org/pdf/2509.05840

Free modules of splines on edge-labeled graphs over $k[x,y]$
We first prove that the ring of graph splines over an edge-labeled graph is isomorphic to the limit of a diagram associated to the edge-labeled graph. This is used to establish a local--global principle for graph splines. We then use this to prove that the module of graph splines on an edge-labeled graph over $k[x,y]$ is free when the graph is locally trivial or determined by a cycle over suitable open sets. Finally, we describe how deletion and contraction on an edge-labeled graph affect the s…

Universal Graph Learning for Power System Reconfigurations: Transfer Across Topology Variations
Tong Wu, Anna Scaglione, Sandy Miguel, Daniel Arnold
https://arxiv.org/abs/2509.08672

Universal Graph Learning for Power System Reconfigurations: Transfer Across Topology Variations
This work addresses a fundamental challenge in applying deep learning to power systems: developing neural network models that transfer across significant system changes, including networks with entirely different topologies and dimensionalities, without requiring training data from unseen reconfigurations. Despite extensive research, most ML-based approaches remain system-specific, limiting real-world deployment. This limitation stems from a dual barrier. First, topology changes shift feature d…

The linearized translator equation and applications
Kyeongsu Choi, Robert Haslhofer, Or Hershkovits
https://arxiv.org/abs/2509.06667 https://arxiv.org/pdf/…

The linearized translator equation and applications
In this paper, we consider the linearized translator equation $L_ϕu=f$, around entire convex translators $M=\textrm{graph}(ϕ)\subset\mathbb{R}^4$, i.e. in the first dimension where the Bernstein property fails. Here, $L_ϕu=\mathrm{div} (a_ϕD u)+ b_ϕ\cdot Du$ is a mean curvature type elliptic operator, whose coefficients degenerate as the slope tends to infinity. We derive two fundamental barrier estimates, specifically an upper-lower estimate and an inner-outer estimate, which allow to pro…

How Fast Can Graph Computations Go on Fine-grained Parallel Architectures
Yuqing Wang, Charles Colley, Brian Wheatman, Jiya Su, David F. Gleich, Andrew A. Chien
https://arxiv.org/abs/2507.00949

How Fast Can Graph Computations Go on Fine-grained Parallel Architectures
Large-scale graph problems are of critical and growing importance and historically parallel architectures have provided little support. In the spirit of co-design, we explore the question, How fast can graph computing go on a fine-grained architecture? We explore the possibilities of an architecture optimized for fine-grained parallelism, natural programming, and the irregularity and skew found in real-world graphs. Using two graph benchmarks, PageRank (PR) and Breadth-First Search (BFS), we ev…

On the $\ell^2$-Betti numbers and algebraic fibring of the (outer) automorphism group of a right-angled Artin group
Marcos Escart\'in-Ferrer
https://arxiv.org/abs/2509.06587

On the $\ell^2$-Betti numbers and algebraic fibring of the (outer) automorphism group of a right-angled Artin group
We compute the first $\ell^2$-Betti number of the automorphism and outer automorphism groups of arbitrary right-angled Artin groups (RAAGs), providing a complete characterization of when it is non-zero. In addition, we determine all $\ell^2$-Betti numbers of the outer automorphism group in the case where the defining graph is disconnected and the associated RAAG is not isomorphic to a free group. We also analyse the algebraic fibring of the pure symmetric automorphism groups $\mathrm{PSA}(A_Γ)…

Planar Stories of Graph Drawings: Algorithms and Experiments
Carla Binucci, Sabine Cornelsen, Walter Didimo, Seok-Hee Hong, Eleni Katsanou, Maurizio Patrignani, Antonios Symvonis, Samuel Wolf
https://arxiv.org/abs/2508.17532

Planar Stories of Graph Drawings: Algorithms and Experiments
We address the problem of computing a dynamic visualization of a geometric graph $G$ as a sequence of frames. Each frame shows only a portion of the graph but their union covers $G$ entirely. The two main requirements of our dynamic visualization are: $(i)$ guaranteeing drawing stability, so to preserve the user's mental map; $(ii)$ keeping the visual complexity of each frame low. To satisfy the first requirement, we never change the position of the vertices. Regarding the second requirement, w…

The rapidly growing number of days with a temperature above 35°C somewhere in the Netherlands:
19 in the 20th century.
39 in the first quarter of this century, and counting. https://www.nu.nl/klimaat/6361334/afzien-in-verzeng…

Afzien in verzengende hitte, dat noem ik nou klimaatrealisme
In de rubriek De broeikas schrijft klimaatverslaggever Jeroen Kraan wekelijks over wat hem opvalt. Deze week: eerdere generaties Nederlanders kenden geen hitte zoals wij deze week meemaakten. Helaas is er geen natuurwet die bij deze extremen een grens trekt.

Pangenome-guided sequence assembly via binary optimisation
Josh Cudby, James Bonfield, Chenxi Zhou, Richard Durbin, Sergii Strelchuk
https://arxiv.org/abs/2508.08200 https://

Pangenome-guided sequence assembly via binary optimisation
De novo genome assembly is challenging in highly repetitive regions; however, reference-guided assemblers often suffer from bias. We propose a framework for pangenome-guided sequence assembly, which can resolve short-read data in complex regions without bias towards a single reference genome. Our method frames assembly as a graph traversal optimisation problem, which can be implemented on quantum computers. The pipeline first annotates pangenome graphs with estimated copy numbers for each node,…

TEn-CATS: Text-Enriched Audio-Visual Video Parsing with Multi-Scale Category-Aware Temporal Graph
Yaru Chen, Faegheh Sardari, Peiliang Zhang, Ruohao Guo, Yang Xiang, Zhenbo Li, Wenwu Wang
https://arxiv.org/abs/2509.04086

TEn-CATS: Text-Enriched Audio-Visual Video Parsing with Multi-Scale Category-Aware Temporal Graph
Audio-Visual Video Parsing (AVVP) task aims to identify event categories and their occurrence times in a given video with weakly supervised labels. Existing methods typically fall into two categories: (i) designing enhanced architectures based on attention mechanism for better temporal modeling, and (ii) generating richer pseudo-labels to compensate for the absence of frame-level annotations. However, the first type methods treat noisy segment-level pseudo labels as reliable supervision and the…

Situationally-aware Path Planning Exploiting 3D Scene Graphs
Saad Ejaz, Marco Giberna, Muhammad Shaheer, Jose Andres Millan-Romera, Ali Tourani, Paul Kremer, Holger Voos, Jose Luis Sanchez-Lopez
https://arxiv.org/abs/2508.06283

Situationally-aware Path Planning Exploiting 3D Scene Graphs
3D Scene Graphs integrate both metric and semantic information, yet their structure remains underutilized for improving path planning efficiency and interpretability. In this work, we present S-Path, a situationally-aware path planner that leverages the metric-semantic structure of indoor 3D Scene Graphs to significantly enhance planning efficiency. S-Path follows a two-stage process: it first performs a search over a semantic graph derived from the scene graph to yield a human-understandable h…

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

Integral Cayley graphs over a nonabelian group of order $8n$
Bei Ye, Xiaogang Liu
https://arxiv.org/abs/2508.10653 https://arxiv.org/pdf/2508.10653

Integral Cayley graphs over a nonabelian group of order $8n$
A graph is called an integral graph when all eigenvalues of its adjacency matrix are integers. We study which Cayley graphs over a nonabelian group $$ T_{8n}=\left\langle a,b\mid a^{2n}=b^8=e,a^n=b^4,b^{-1}ab=a^{-1} \right \rangle $$ are integral graphs. Based on the group representation theory, we first give the irreducible matrix representations and characters of $T_{8n}$. Then we give necessary and sufficient conditions for which Cayley graphs over $T_{8n}$ are integral graphs. As applicatio…

On the Effectiveness of Graph Reordering for Accelerating Approximate Nearest Neighbor Search on GPU
Yutaro Oguri, Mai Nishimura, Yusuke Matsui
https://arxiv.org/abs/2508.15436 …

On the Effectiveness of Graph Reordering for Accelerating Approximate Nearest Neighbor Search on GPU
We present the first systematic investigation of graph reordering effects for graph-based Approximate Nearest Neighbor Search (ANNS) on a GPU. While graph-based ANNS has become the dominant paradigm for modern AI applications, recent approaches focus on algorithmic innovations while neglecting memory layout considerations that significantly affect execution time. Our unified evaluation framework enables comprehensive evaluation of diverse reordering strategies across different graph indices thr…

Revisiting Graph Analytics Benchmark
Lingkai Meng, Yu Shao, Long Yuan, Longbin Lai, Peng Cheng, Xue Li, Wenyuan Yu, Wenjie Zhang, Xuemin Lin, Jingren Zhou
https://arxiv.org/abs/2506.21811

Revisiting Graph Analytics Benchmark
The rise of graph analytics platforms has led to the development of various benchmarks for evaluating and comparing platform performance. However, existing benchmarks often fall short of fully assessing performance due to limitations in core algorithm selection, data generation processes (and the corresponding synthetic datasets), as well as the neglect of API usability evaluation. To address these shortcomings, we propose a novel graph analytics benchmark. First, we select eight core algorithm…

Combining Performance and Productivity: Accelerating the Network Sensing Graph Challenge with GPUs and Commodity Data Science Software
Siddharth Samsi, Dan Campbell, Emanuel Scoullos, Oded Green
https://arxiv.org/abs/2509.03653

Combining Performance and Productivity: Accelerating the Network Sensing Graph Challenge with GPUs and Commodity Data Science Software
The HPEC Graph Challenge is a collection of benchmarks representing complex workloads that test the hardware and software components of HPC systems, which traditional benchmarks, such as LINPACK, do not. The first benchmark, Subgraph Isomorphism, focused on several compute-bound and memory-bound kernels. The most recent of the challenges, the Anonymized Network Sensing Graph Challenge, represents a shift in direction, as it represents a longer end-to-end workload that requires many more softwar…

A Graph-Based Test-Harness for LLM Evaluation
Jessica Lundin, Guillaume Chabot-Couture
https://arxiv.org/abs/2508.20810 https://arxiv.org/pdf/2508.20810

A Graph-Based Test-Harness for LLM Evaluation
We present a first known prototype of a dynamic, systematic benchmark of medical guidelines for 400+ questions, with 3.3+ trillion possible combinations, covering 100\% of guideline relationships. We transformed the WHO IMCI handbook into a directed graph with 200+ nodes (conditions, symptoms, treatments, follow-ups, severities) and 300+ edges, then used graph traversal to generate questions that incorporated age-specific scenarios and contextual distractors to ensure clinical relevance. Our gr…

Testing Depth First Search Numbering
Artur Czumaj, Christian Sohler, Stefan Walzer
https://arxiv.org/abs/2509.05132 https://arxiv.org/pdf/2509.05132…

Testing Depth First Search Numbering
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with sublinear query complexity. Here, a graph property P is testable with a sublinear query complexity if there is an algorithm that makes a sublinear number of queries to the input graph and accepts with probability at least 2/3, if the graph has property P, and reje…

Causal Graph Fuzzy LLMs: A First Introduction and Applications in Time Series Forecasting
Omid Orang, Patricia O. Lucas, Gabriel I. F. Paiva, Petronio C. L. Silva, Felipe Augusto Rocha da Silva, Adriano Alonso Veloso, Frederico Gadelha Guimaraes
https://arxiv.org/abs/2507.17016

Causal Graph Fuzzy LLMs: A First Introduction and Applications in Time Series Forecasting
In recent years, the application of Large Language Models (LLMs) to time series forecasting (TSF) has garnered significant attention among researchers. This study presents a new frame of LLMs named CGF-LLM using GPT-2 combined with fuzzy time series (FTS) and causal graph to predict multivariate time series, marking the first such architecture in the literature. The key objective is to convert numerical time series into interpretable forms through the parallel application of fuzzification and c…

Facet: highly efficient E(3)-equivariant networks for interatomic potentials
Nicholas Miklaucic, Lai Wei, Rongzhi Dong, Nihang Fu, Sadman Sadeed Omee, Qingyang Li, Sourin Dey, Victor Fung, Jianjun Hu
https://arxiv.org/abs/2509.08418

Facet: highly efficient E(3)-equivariant networks for interatomic potentials
Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions…

Information-Theoretic Graph Fusion with Vision-Language-Action Model for Policy Reasoning and Dual Robotic Control
Shunlei Li, Longsen Gao, Jin Wang, Chang Che, Xi Xiao, Jiuwen Cao, Yingbai Hu, Hamid Reza Karimi
https://arxiv.org/abs/2508.05342

Information-Theoretic Graph Fusion with Vision-Language-Action Model for Policy Reasoning and Dual Robotic Control
Teaching robots dexterous skills from human videos remains challenging due to the reliance on low-level trajectory imitation, which fails to generalize across object types, spatial layouts, and manipulator configurations. We propose Graph-Fused Vision-Language-Action (GF-VLA), a framework that enables dual-arm robotic systems to perform task-level reasoning and execution directly from RGB and Depth human demonstrations. GF-VLA first extracts Shannon-information-based cues to identify hands and …

A graph energy conjecture through the lenses of semidefinite programming
Aida Abiad, Gabriel Coutinho, Emanuel Juliano, Luuk Reijnders
https://arxiv.org/abs/2509.05814 https://

A graph energy conjecture through the lenses of semidefinite programming
Let $G$ be a graph on $n$ vertices with independence number $α(G)$. Let $\mathcal{E}(G)$ be the energy of a graph, defined as the sum of the absolute values of the adjacency eigenvalues of $G$. Using Graffiti, Fajtlowicz conjectured in the 1980s that $$\frac{1}{2}\mathcal{E}(G) \geq n - α(G).$$ In this paper we derive a semidefinite program formulation of the graph energy, and we use it to obtain several results that constitute a first step towards proving this conjecture. In particular, we s…

Hierarchical Graph Neural Network for Compressed Speech Steganalysis
Mustapha Hemis, Hamza Kheddar, Mohamed Chahine Ghanem, Bachir Boudraa
https://arxiv.org/abs/2507.21591 https…

Hierarchical Graph Neural Network for Compressed Speech Steganalysis
Steganalysis methods based on deep learning (DL) often struggle with computational complexity and challenges in generalizing across different datasets. Incorporating a graph neural network (GNN) into steganalysis schemes enables the leveraging of relational data for improved detection accuracy and adaptability. This paper presents the first application of a Graph Neural Network (GNN), specifically the GraphSAGE architecture, for steganalysis of compressed voice over IP (VoIP) speech streams. Th…

On damping a delay control system with global contraction on a temporal graph
Aleksandr Lednov
https://arxiv.org/abs/2509.02608 https://arxiv.org/pdf/2509.…

On damping a delay control system with global contraction on a temporal graph
We consider the problem of damping a control system with delay described by first-order functional-differential equations on a temporal tree. The delay in the system is time-proportional and propagates through the internal vertices. The problem of minimizing the energy functional with account of the probabilities of the scenarios corresponding to different edges is studied. We establish the equivalence of this variational problem to a certain boundary value problem for second-order functional-d…

Jet Schemes, Newton Polygons and Continued Fractions
Ghadi Abdallah, Maximiliano Leyton-\'Alvarez, Bassam Mourad, Hussein Mourtada
https://arxiv.org/abs/2509.06095 https://

Jet Schemes, Newton Polygons and Continued Fractions
We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the lattice points in the first quadrant of the Cartesian plane. In particular, we determine all the irreducible components of the jet schemes. Furthermore, we prove that this subgraph encodes the embedded topological type of the curve singularity in the plane. Finally, we introduce a generating series defined in terms o…

Weakly branch actions: first-order theory, rigidity and Boston's conjecture
Jorge Fari\~na-Asategui
https://arxiv.org/abs/2507.22507 https://arxiv.org/…

Weakly branch actions: first-order theory, rigidity and Boston's conjecture
We disprove a well-known conjecture of Boston (2000), which claims that a just-infinite pro-$p$ group is branch if and only if it admits a positive-dimensional embedding in the group of $p$-adic automorphisms. This is obtained as a result of a comprehensive study of the rigidity of branch actions. Firstly, we generalize the notion of the structure graph, introduced by Wilson in 2000, to weakly branch groups and use it to prove several results on the first-order theory of weakly branch groups,…

How Complex is a Complex Network? Insights from Linear Systems Theory
Giacomo Baggio, Marco Fabris
https://arxiv.org/abs/2507.06389 https://

How Complex is a Complex Network? Insights from Linear Systems Theory
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the effect of nodal dynamics in the interconnected system, we propose a new quantitative index of network complexity rooted in the notion of McMillan degree of a linear system. First, we show that network systems with the same interconnection structure share the s…

Efficient Catalytic Graph Algorithms
James Cook, Edward Pyne
https://arxiv.org/abs/2509.06209 https://arxiv.org/pdf/2509.06209

Efficient Catalytic Graph Algorithms
We give fast, simple, and implementable catalytic logspace algorithms for two fundamental graph problems. First, a randomized catalytic algorithm for $s\to t$ connectivity running in $\widetilde{O}(nm)$ time, and a deterministic catalytic algorithm for the same running in $\widetilde{O}(n^3 m)$ time. The former algorithm is the first algorithmic use of randomization in $\mathsf{CL}$. The algorithm uses one register per vertex and repeatedly ``pushes'' values along the edges in the graph. Se…

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

On the multiplicity of 1 as a Laplacian eigenvalue of a graph
Fenglei Tian, Dein Wong
https://arxiv.org/abs/2507.06184 https://arxiv.…

On the multiplicity of 1 as a Laplacian eigenvalue of a graph
Let $G$ be a graph with $p(G)$ pendant vertices and $q(G)$ quasi-pendant vertices. Denote by $m_{L(G)}(λ)$ the multiplicity of $λ$ as a Laplacian eigenvalue of $G$. Let $\overline{G}$ be the reduced graph of $G$, which can be obtained from $G$ by deleting some pendant vertices such that $p(\overline{G})=q(\overline{G})$. We first prove that $m_{L(G)}(1)=p(G)-q(G)+m_{L(\overline{G})}(1)$. Since deleting pendant path $P_3$ does not change the multiplicity of Laplacian eigenvalue 1 of a graph, w…

Higher-Order Graph Databases
Maciej Besta, Shriram Chandran, Jakub Cudak, Patrick Iff, Marcin Copik, Robert Gerstenberger, Tomasz Szydlo, J\"urgen M\"uller, Torsten Hoefler
https://arxiv.org/abs/2506.19661

Higher-Order Graph Databases
Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as subgraph counting, polyadic modeling, and HO graph learning. We address this by introducing a new class of systems, higher-order graph databases (HO-GDBs) that use lifting and lowering paradigms to seamlessly extend traditional GDBs with HO. We provide a theore…

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

NaviX: A Native Vector Index Design for Graph DBMSs With Robust Predicate-Agnostic Search Performance
Gaurav Sehgal, Semih Salihoglu
https://arxiv.org/abs/2506.23397

NaviX: A Native Vector Index Design for Graph DBMSs With Robust Predicate-Agnostic Search Performance
There is an increasing demand for extending existing DBMSs with vector indices so that they become unified systems capable of supporting modern predictive applications, which require joint querying of vector embeddings together with the structured properties and connections of objects. We present NaviX, a native vector index for graph DBMSs (GDBMSs) that has two main design goals. First, we aim to implement a disk-based vector index that leverages the core storage and query-processing capabilit…

Spiking Variational Graph Representation Inference for Video Summarization
Wenrui Li, Wei Han, Liang-Jian Deng, Ruiqin Xiong, Xiaopeng Fan
https://arxiv.org/abs/2508.15389 https…

Spiking Variational Graph Representation Inference for Video Summarization
With the rise of short video content, efficient video summarization techniques for extracting key information have become crucial. However, existing methods struggle to capture the global temporal dependencies and maintain the semantic coherence of video content. Additionally, these methods are also influenced by noise during multi-channel feature fusion. We propose a Spiking Variational Graph (SpiVG) Network, which enhances information density and reduces computational complexity. First, we de…

Automated discovery of finite volume schemes using Graph Neural Networks
Paul Garnier, Jonathan Viquerat, Elie Hachem
https://arxiv.org/abs/2508.19052 https://

Automated discovery of finite volume schemes using Graph Neural Networks
Graph Neural Networks (GNNs) have deeply modified the landscape of numerical simulations by demonstrating strong capabilities in approximating solutions of physical systems. However, their ability to extrapolate beyond their training domain (\textit{e.g.} larger or structurally different graphs) remains uncertain. In this work, we establish that GNNs can serve purposes beyond their traditional role, and be exploited to generate numerical schemes, in conjunction with symbolic regression. First, …

Online Dynamic SLAM with Incremental Smoothing and Mapping
Jesse Morris, Yiduo Wang, Viorela Ila
https://arxiv.org/abs/2509.08197 https://arxiv.org/pdf/250…

Online Dynamic SLAM with Incremental Smoothing and Mapping
Dynamic SLAM methods jointly estimate for the static and dynamic scene components, however existing approaches, while accurate, are computationally expensive and unsuitable for online applications. In this work, we present the first application of incremental optimisation techniques to Dynamic SLAM. We introduce a novel factor-graph formulation and system architecture designed to take advantage of existing incremental optimisation methods and support online estimation. On multiple datasets, we …

Graph Representation-based Model Poisoning on Federated LLMs in CyberEdge Networks
Hanlin Cai, Haofan Dong, Houtianfu Wang, Kai Li, Ozgur B. Akan
https://arxiv.org/abs/2507.01694 …

Graph Representation-based Model Poisoning on Federated LLMs in CyberEdge Networks
Federated large language models (FedLLMs) provide powerful generative capabilities in CyberEdge networks while protecting data privacy. However, FedLLMs remains highly vulnerable to model poisoning attacks. This article first reviews recent model poisoning techniques and existing defense mechanisms for FedLLMs, highlighting critical limitations, particularly under non-IID text distributions. In particular, current defenses primarily utilize distance-based outlier detection or norm constraints, …

On a Conjecture about Comparing the First and Second Zagreb Indices of Graphs
Ali Ghalavand
https://arxiv.org/abs/2509.07434 https://arxiv.org/pdf/2509.074…

On a Conjecture about Comparing the First and Second Zagreb Indices of Graphs
Let $G$ be a graph with order $n(G)$, size $m(G)$, first Zagreb index $M_1(G)$, and second Zagreb index $M_2(G)$. More than twenty years ago, it was conjectured that $\frac{M_1(G)}{n(G)} \leq \frac{M_2(G)}{m(G)}$. Later, Hansen and Vukičević demonstrated that this conjecture does not hold for general graphs but is valid for chemical graphs. In this paper, as an extension of the study of chemical graphs, we investigate graphs in which the difference between the minimum and maximum degrees is a…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
Mohsen Ghaffari, Jaehyun Koo
https://arxiv.org/abs/2507.06338 https://…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
This paper presents the first parallel batch-dynamic algorithms for computing spanners and sparsifiers. Our algorithms process any batch of edge insertions and deletions in an $n$-node undirected graph, in $\text{poly}(\log n)$ depth and using amortized work near-linear in the batch size. Our concrete results are as follows: - Our base algorithm maintains a spanner with $(2k-1)$ stretch and $\tilde{O}(n^{1+1/k})$ edges, for any $k\geq 1$. - Our first extension maintains a sparse spanner wit…

Property O and Erd\H{o}s--Szekeres properties in linear hypergraphs
Suyun Jiang, Ander Lamaison, Minghui Ouyang
https://arxiv.org/abs/2509.08692 https://ar…

Property O and Erdős--Szekeres properties in linear hypergraphs
An oriented $k$-uniform hypergraph, or oriented $k$-graph, is said to satisfy Property O if, for every linear ordering of its vertex set, there is some edge oriented consistently with this order. The minimum number $f(k)$ of edges in a $k$-graph with Property O was first studied by Duffus, Kay, and Rödl, and later improved by Kronenberg, Kusch, Lamaison, Micek, and Tran. In particular, they established the bounds $k! + 1 \le f(k) \le \left(\lfloor\tfrac{k}{2}\rfloor+1 \right) k! - \lfloor\tfra…

football_tsevans: NCAA college football 2000 (corrected metadata)
A network of American football games between Division IA colleges during regular season Fall 2000. This version contains some corrections made by T. S. Evans, in particular:.
This network has 115 nodes and 613 edges.
Tags: Social, Sports, Unweighted
https://

Improved Algorithms for Effective Resistance Computation on Graphs
Yichun Yang, Rong-Hua Li, Meihao Liao, Guoren Wang
https://arxiv.org/abs/2507.04674 http…

Improved Algorithms for Effective Resistance Computation on Graphs
Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges. First, we focus on local online-computation algorithms for ER approximation, aiming to improve the dependency on the approximation error parameter $ε$. Specifically, for a given vertex pair $(s,t)$, we propose a local algorithm with a time complexity of $\tilde{O…

On two-distance-transitive graphs
Wei Jin, Jack H. Koolen, Chenhui Lv
https://arxiv.org/abs/2508.02010 https://arxiv.org/pdf/2508.02010

On two-distance-transitive graphs
A $2$-distance-transitive graph is a vertex-transitive graph whose vertex stabilizer is transitive on both the first step and the second step neighborhoods. In this paper, we first answer a question of A. Devillers, M. Giudici, C. H. Li and C. E. Praeger in 2012 about vertex-quasiprimitive $2$-distance-transitive graphs for the odd order case. Then we characterize $2$-distance-transitive graphs of valency $p$ or $p+1$ where $p$ is a prime. After that, as an application of the above result, we c…

Simple Algorithms for Fully Dynamic Edge Connectivity
Yotam Kenneth-Mordoch, Robert Krauthgamer
https://arxiv.org/abs/2508.07783 https://arxiv.org/pdf/2508…

Simple Algorithms for Fully Dynamic Edge Connectivity
In the fully dynamic edge connectivity problem, the input is a simple graph $G$ undergoing edge insertions and deletions, and the goal is to maintain its edge connectivity, denoted $λ_G$. We present two simple randomized algorithms solving this problem. The first algorithm maintains the edge connectivity in worst-case update time $\tilde{O}(n)$ per edge update, matching the known bound but with simpler analysis. Our second algorithm achieves worst-case update time $\tilde{O}(n/λ_G)$ and worst…

A Cop-Win Graph with Maximum Capture Time $\omega$
Tom\'a\v{s} Fl\'idr, Maria-Romina Ivan
https://arxiv.org/abs/2507.22276 https://arxiv.org/pdf/25…

A Cop-Win Graph with Maximum Capture Time $ω$
The game of cops and robbers is played on a fixed (finite or infinite) graph $G$. The cop chooses his starting position, then the robber chooses his. After that, they take turns and move to adjacent vertices, or stay at their current vertex, with the cop moving first. The game finishes if the cop lands on the robber's vertex. In that case we say that the cop wins, while if the robber is never caught then we say that the robber wins. The graph $G$ is called cop-win if the cop has a winning strat…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Avi Kadria, Liam Roditty
https://arxiv.org/abs/2507.06721 https://arxiv.org/p…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first algorithm runs in $\Ot(\max(n^{1+2/k}, m^{1-\frac{1}{k-1}}n^{\frac{2}{k-1}}))$ time, and improves upon the $\Ot(\min(mn^{\frac{1}{k}},n^2))$ time of Thorup and Zwick [STOC 2001, JACM 2005] and Baswana and Kavitha [FOCS 2006, SICOMP 2010], for every $k > 2$ and $…

On graphs, homology bases, and triangulated homology spheres
Karim Adiprasito, Marc Lackenby, Juan Souto, Geva Yashfe
https://arxiv.org/abs/2509.06275 https://

On graphs, homology bases, and triangulated homology spheres
We describe a construction that takes as input a graph and a basis for its first homology, and returns a triangulation of a 3-dimensional homology sphere. This makes precise an idea of M. Gromov and A. Nabutovski. The immediate application, essentially described by Gromov, is to translate problems about asymptotics of homology sphere triangulations to asymptotic counting problems for constant-degree graphs with "short" homology bases. We construct families of 3- sphere triangulations with dual …

Asymptotic enumeration of graph factors by cumulant expansion
Mikhail Isaev, Brendan D. McKay
https://arxiv.org/abs/2508.18731 https://arxiv.org/pdf/2508.1…

Asymptotic enumeration of graph factors by cumulant expansion
Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence $\boldsymbol d$ to arbitrary precision. The average degree can be any power of $n$ and the variation in degrees can be very large. The method uses an explicit bound on the tail of the cumulant generating function found by the first author. As a first application, w…

Size of bipartite graphs with given diameter and connectivity constraints
Sonwabile Mafunda
https://arxiv.org/abs/2509.01825 https://arxiv.org/pdf/2509.018…

Size of bipartite graphs with given diameter and connectivity constraints
In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter $d$, and connectivity $κ$. It was shown by Ali, Mazorodze, Mukwembi and Vetrík [On size, order, diameter and edge-connectivity of graphs. Acta Math. Hungar. {\bf 152}, (2017)] that for a connected triangle-free graph of order $n$, diameter $d$ and edge-connectivity $λ$, the size is bounded from above by about $\frac{1}{4}\left(n-\frac{(λ+c) d}{2}\right)^2…

Counter-example to Conjectures on Complemented Zero-Divisor Graphs of Semigroups
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
https://arxiv.org/abs/2506.16919

Counter-example to Conjectures on Complemented Zero-Divisor Graphs of Semigroups
In this paper, we are motivated by two conjectures proposed by C. Bender et al.\ in 2024, which have remained open questions. The first conjecture states that if the complemented zero-divisor graph \( G(S) \) of a commutative semigroup \( S \) with a zero element has the clique number three or greater, then the reduced graph \( G_r(S) \) is isomorphic to the graph \( G(\mathcal{P}(n)) \). The second conjecture asserts that if \( G(S) \) is a complemented zero-divisor graph with the clique numbe…