Tootfinder

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web

Optimally building spanning graphs in semirandom graph processes
Michael Anastos, Maur\'icio Collares, Joshua Erde, Mihyun Kang, Dominik Schmid, Gregory B. Sorkin
https://arxiv.org/abs/2509.26028

Optimally building spanning graphs in semirandom graph processes
The semirandom graph process constructs a graph $G$ in a series of rounds, starting with the empty graph on $n$ vertices. In each round, a player is offered a vertex $v$ chosen uniformly at random, and chooses an edge on $v$ to add to $G$. The player's aim is to make $G$ satisfy some property as quickly as possible. Our interest is in the property that $G$ contain a given $n$-vertex graph $H$ with maximum degree $Δ$. In 2021, Ben-Eliezer, Gishboliner, Hefetz and Krivelevich showed that there i…

@… TiL about the Petersen Graph, which is the exact combination of mathematics and pentagrams that I feel epitomises The Laundry Files.
https://en.wikipedia.org/wiki/Petersen

Petersen graph - Wikipedia

Cost-aware Photonic Graph State Generation: A Graphical Framework
Sobhan Ghanbari, Hoi-Kwong Lo
https://arxiv.org/abs/2509.22777 https://arxiv.org/pdf/2509…

Cost-aware Photonic Graph State Generation: A Graphical Framework
Photonic graph states are essential resources for quantum computation and communication. Deterministic emitter-based generation of graph states overcomes the scalability issues of probabilistic approaches, but their experimental realization is constrained by technological demands, often expressed by the number of two-qubit gates and the depth and/or width of the quantum circuits used to model the generation process. We introduce a cost-aware framework for the generation of photonic graph states…

Graph Distribution-valued Signals: A Wasserstein Space Perspective
Yanan Zhao, Feng Ji, Xingchao Jian, Wee Peng Tay
https://arxiv.org/abs/2509.25802 https://

Graph Distribution-valued Signals: A Wasserstein Space Perspective
We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of classical vector-based GSP, including the assumption of synchronous observations over vertices, the inability to capture uncertainty, and the requirement for strict correspondence in graph filtering. By representing signals as distributions, GDSs naturally encode …

Convergence of graph Dirichlet energies and graph Laplacians on intersecting manifolds of varying dimensions
Leon Bungert, Dejan Slep\v{c}ev
https://arxiv.org/abs/2509.24458 htt…

Convergence of graph Dirichlet energies and graph Laplacians on intersecting manifolds of varying dimensions
We study $Γ$-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on unions of intersecting manifolds of potentially different dimensions. Our investigation is motivated by problems of machine learning, as real-world data often consist of parts or classes with different intrinsic dimensions. An important challenge is to understand which machine learning methods adapt to such varied dimensionalities. We investigate the standard unnormalized and the normalized gra…

Accelerating Dynamic Image Graph Construction on FPGA for Vision GNNs
Anvitha Ramachandran, Dhruv Parikh, Viktor Prasanna
https://arxiv.org/abs/2509.25121 https://

Accelerating Dynamic Image Graph Construction on FPGA for Vision GNNs
Vision Graph Neural Networks (Vision GNNs, or ViGs) represent images as unstructured graphs, achieving state of the art performance in computer vision tasks such as image classification, object detection, and instance segmentation. Dynamic Image Graph Construction (DIGC) builds image graphs by connecting patches (nodes) based on feature similarity, and is dynamically repeated in each ViG layer following GNN based patch (node) feature updates. However, DIGC constitutes over 50% of end to end ViG…

My post traveling through the #Fediverse got another push over the weekend (thx @…), motivating me to have another look. And surprise: After adding the software of multiple instances,

Another month, another column! Can you tell when someone loaned me an ebike and when I got my own and started to ride to work?
I went into 2025 hoping to do 1,000 miles, realized half way through I could probably hit 1,200 miles and now with 3 months left I'm over 1,400 miles.
#ebike #bikeTooter

OntoAligner Meets Knowledge Graph Embedding Aligners
Hamed Babaei Giglou, Jennifer D'Souza, S\"oren Auer, Mahsa Sanaei
https://arxiv.org/abs/2509.26417 https://

OntoAligner Meets Knowledge Graph Embedding Aligners
Ontology Alignment (OA) is essential for enabling semantic interoperability across heterogeneous knowledge systems. While recent advances have focused on large language models (LLMs) for capturing contextual semantics, this work revisits the underexplored potential of Knowledge Graph Embedding (KGE) models, which offer scalable, structure-aware representations well-suited to ontology-based tasks. Despite their effectiveness in link prediction, KGE methods remain underutilized in OA, with most p…

Graph-based Analysis for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays
M. Alakhras, S. M. S. Movahed
https://arxiv.org/abs/2509.24904 https://…

Graph-based Analysis for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays
The stochastic gravitational wave background (SGWB) reveals valuable information about its origin and the Universe. The pulsar timing arrays (PTAs) are suitable indicators for detecting SGWB within the nano-Hertz frequency range. In this work, we propose a graph-based method implemented on the pulsar timing residuals (PTRs) for SGWB detection and examining uncertainties of its parameters. We construct a correlation graph with pulsars as its nodes, and analyze the graph-based summary statistics,…

Efficient and Transferable Agentic Knowledge Graph RAG via Reinforcement Learning
Jinyeop Song, Song Wang, Julian Shun, Yada Zhu
https://arxiv.org/abs/2509.26383 https://…

Efficient and Transferable Agentic Knowledge Graph RAG via Reinforcement Learning
Knowledge-graph retrieval-augmented generation (KG-RAG) couples large language models (LLMs) with structured, verifiable knowledge graphs (KGs) to reduce hallucinations and expose reasoning traces. However, many KG-RAG systems compose multiple LLM modules (e.g planning, reasoning, and responding), inflating inference cost and binding behavior to a specific target KG. To address this, we introduce KG-R1, an agentic KG retrieval-augmented generation (KG-RAG) framework through reinforcement learni…

SGNNBench: A Holistic Evaluation of Spiking Graph Neural Network on Large-scale Graph
Huizhe Zhang, Jintang Li, Yuchang Zhu, Liang Chen, Li Kuang
https://arxiv.org/abs/2509.21342

SGNNBench: A Holistic Evaluation of Spiking Graph Neural Network on Large-scale Graph
Graph Neural Networks (GNNs) are exemplary deep models designed for graph data. Message passing mechanism enables GNNs to effectively capture graph topology and push the performance boundaries across various graph tasks. However, the trend of developing such complex machinery for graph representation learning has become unsustainable on large-scale graphs. The computational and time overhead make it imperative to develop more energy-efficient GNNs to cope with the explosive growth of real-world…

Graphite: A GPU-Accelerated Mixed-Precision Graph Optimization Framework
Shishir Gopinath, Karthik Dantu, Steven Y. Ko
https://arxiv.org/abs/2509.26581 https://

Graphite: A GPU-Accelerated Mixed-Precision Graph Optimization Framework
We present Graphite, a GPU-accelerated nonlinear graph optimization framework. It provides a CUDA C++ interface to enable the sharing of code between a realtime application, such as a SLAM system, and its optimization tasks. The framework supports techniques to reduce memory usage, including in-place optimization, support for multiple floating point types and mixed-precision modes, and dynamically computed Jacobians. We evaluate Graphite on well-known bundle adjustment problems and find that it…

Sparse Graph Reconstruction and Seriation for Large-Scale Image Stacks
Fuming Yang, Yaron Meirovitch, Jeff W. Lichtman
https://arxiv.org/abs/2509.23084 https://

Sparse Graph Reconstruction and Seriation for Large-Scale Image Stacks
We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that provably builds a sparse graph containing all edges needed for exact seriation using only O(N(log N + K)) oracle queries, which is near-linear in N for fixed window K. The approach is parallelizable and supports both binary and bounded-noise distance oracles. Our fi…

DeepProv: Behavioral Characterization and Repair of Neural Networks via Inference Provenance Graph Analysis
Firas Ben Hmida, Abderrahmen Amich, Ata Kaboudi, Birhanu Eshete
https://arxiv.org/abs/2509.26562

DeepProv: Behavioral Characterization and Repair of Neural Networks via Inference Provenance Graph Analysis
Deep neural networks (DNNs) are increasingly being deployed in high-stakes applications, from self-driving cars to biometric authentication. However, their unpredictable and unreliable behaviors in real-world settings require new approaches to characterize and ensure their reliability. This paper introduces DeepProv, a novel and customizable system designed to capture and characterize the runtime behavior of DNNs during inference by using their underlying graph structure. Inspired by system a…

This graph perfectly illustrates how bad the Raiders have been on both sides of the ball https://raiderswire.usatoday.com/story/sports/nfl/raiders/2025/10/30/raiders-offense-defense-epa-graph-turnover-differe…

A construction of simple-minded systems over domestic Brauer graph algebras
Zhen Zhang
https://arxiv.org/abs/2509.24184 https://arxiv.org/pdf/2509.24184

A construction of simple-minded systems over domestic Brauer graph algebras
Let $A$ be a 2-domestic Brauer graph algebra. We present a construction for a family of objects on $A$-$\stmod$ to be a simple-minded system and our construction provides all simple-minded systems on $A$-$\stmod$. As a byproduct, we provide a new proof of AR-conjecture for 2-domestic Brauer graph algebras and we prove that a weakly simple-minded system with a finite cardinality is a simple-minded system on $A$-$\stmod$. We also prove that an orthogonal system $\mathcal{S}$ which contains at lea…

A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph
Shuai Kou, Chengfu Qin, Weihua Yang, Mingzu Zhang, Shuang Zhao
https://arxiv.org/abs/2509.25809

A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph
An edge of a quasi $k$-connected graph is said to be quasi $k$-contractible if the contraction of the edge results in a quasi $k$-connected graph. We show that every 5-connected graph contains a quasi 5-contractible edge. Furthermore, we prove that a quasi 5-connected graph possesses a quasi 5-contractible edge, if the degree sum of any two vertices with distance at most two is at least 9. This result strengthens a theorem proved by Kriesell when $k=4$ (M. Kriesell, A degree sum condition for t…

flickr_aminer: Flickr social graph
This network contains the social graph of flickr, a popular photo sharing network for users to upload photos and share photos, where a directed edge (i,j) means that user i follows user j.
This network has 214626 nodes and 9114557 edges.
Tags: Social, Online, Unweighted
https://

A Graph-based Hybrid Beamforming Framework for MIMO Cell-Free ISAC Networks
Yanan Du, Sai Xu, Jagmohan Chauhan
https://arxiv.org/abs/2509.25385 https://arx…

A Graph-based Hybrid Beamforming Framework for MIMO Cell-Free ISAC Networks
This paper develops a graph-based hybrid beamforming framework for multiple-input multiple-output (MIMO) cell-free integrated sensing and communication (ISAC) networks. Specifically, we construct a novel MIMO cell-free ISAC network model. In this model, multiple dual-function base station (BS) transmitters employ distributed hybrid beamforming to enable simultaneous communication and sensing, while maintaining physical separation between the transmitters and the radar receiver. Building on this…

One Prompt Fits All: Universal Graph Adaptation for Pretrained Models
Yongqi Huang, Jitao Zhao, Dongxiao He, Xiaobao Wang, Yawen Li, Yuxiao Huang, Di Jin, Zhiyong Feng
https://arxiv.org/abs/2509.22416 …

One Prompt Fits All: Universal Graph Adaptation for Pretrained Models
Graph Prompt Learning (GPL) has emerged as a promising paradigm that bridges graph pretraining models and downstream scenarios, mitigating label dependency and the misalignment between upstream pretraining and downstream tasks. Although existing GPL studies explore various prompt strategies, their effectiveness and underlying principles remain unclear. We identify two critical limitations: (1) Lack of consensus on underlying mechanisms: Despite current GPLs have advanced the field, there is no …

Private Information Retrieval over Graphs
Gennian Ge, Hao Wang, Zixiang Xu, Yijun Zhang
https://arxiv.org/abs/2509.26512 https://arxiv.org/pdf/2509.26512…

Private Information Retrieval over Graphs
The problem of PIR in graph-based replication systems has received significant attention in recent years. A systematic study was conducted by Sadeh, Gu, and Tamo, where each file is replicated across two servers and the storage topology is modeled by a graph. The PIR capacity of a graph $G$, denoted by $\mathcal{C}(G)$, is defined as the supremum of retrieval rates achievable by schemes that preserve user privacy, with the rate measured as the ratio between the file size and the total number of…

Rotation sets and axes in the fine curve graph for torus homeomorphisms
Sebastian Hensel, Fr\'ed\'eric Le Roux
https://arxiv.org/abs/2509.26156 https://

Rotation sets and axes in the fine curve graph for torus homeomorphisms
We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A key ingredient is a metric version of the classical WPD property from geometric group theory. As a consequence we find new stable criteria for positive scl, and for two homeomorphisms to generate a free group.

MUSE-Explainer: Counterfactual Explanations for Symbolic Music Graph Classification Models
Baptiste Hilaire, Emmanouil Karystinaios, Gerhard Widmer
https://arxiv.org/abs/2509.26521

MUSE-Explainer: Counterfactual Explanations for Symbolic Music Graph Classification Models
Interpretability is essential for deploying deep learning models in symbolic music analysis, yet most research emphasizes model performance over explanation. To address this, we introduce MUSE-Explainer, a new method that helps reveal how music Graph Neural Network models make decisions by providing clear, human-friendly explanations. Our approach generates counterfactual explanations by making small, meaningful changes to musical score graphs that alter a model's prediction while ensuring the …

Community detection robustness of graph neural networks
Jaidev Goel, Pablo Moriano, Ramakrishnan Kannan, Yulia R. Gel
https://arxiv.org/abs/2509.24662 https://

Community detection robustness of graph neural networks
Graph neural networks (GNNs) are increasingly widely used for community detection in attributed networks. They combine structural topology with node attributes through message passing and pooling. However, their robustness or lack of thereof with respect to different perturbations and targeted attacks in conjunction with community detection tasks is not well understood. To shed light into latent mechanisms behind GNN sensitivity on community detection tasks, we conduct a systematic computationa…

Graph-Based Learning of Free Surface Dynamics in Generalized Newtonian Fluids using Smoothed Particle Hydrodynamics
Hyo-Jin Kim, Jaekwang Kim, Hyung-Jun Park
https://arxiv.org/abs/2509.24264

Graph-Based Learning of Free Surface Dynamics in Generalized Newtonian Fluids using Smoothed Particle Hydrodynamics
In this study, we propose a graph neural network (GNN) model for efficiently predicting the flow behavior of non-Newtonian fluids with free surface dynamics. The numerical analysis of non-Newtonian fluids presents significant challenges, as traditional algorithms designed for Newtonian fluids with constant viscosity often struggle to converge when applied to non-Newtonian cases, where rheological properties vary dynamically with flow conditions. Among these, power-law fluids exhibit viscosity t…

RANGER -- Repository-Level Agent for Graph-Enhanced Retrieval
Pratik Shah, Rajat Ghosh, Aryan Singhal, Debojyoti Dutta
https://arxiv.org/abs/2509.25257 https://

RANGER -- Repository-Level Agent for Graph-Enhanced Retrieval
General-purpose automated software engineering (ASE) includes tasks such as code completion, retrieval, repair, QA, and summarization. These tasks require a code retrieval system that can handle specific queries about code entities, or code entity queries (for example, locating a specific class or retrieving the dependencies of a function), as well as general queries without explicit code entities, or natural language queries (for example, describing a task and retrieving the corresponding code…

👻 Probiert es mal aus, egal ob gruselig oder heilig, der „Geist” erwartet euch (es funktionieren auch andere Suchbegriffe, Notizen oder Bilder 😊 )
🧠 P.S. Für alle #CultureKnowledgeGraph- und #SPARQL-Kenner unter euch, bitte hier entlang 👉

Graph Neural Network Acceleration on FPGAs for Fast Inference in Future Muon Triggers at HL-LHC
Martino Errico (Sapienza Universit\`a di Roma, INFN Sezione di Roma), Davide Fiacco (Sapienza Universit\`a di Roma, INFN Sezione di Roma), Stefano Giagu (Sapienza Universit\`a di Roma, INFN Sezione di Roma), Giuliano Gustavino (Sapienza Universit\`a di Roma, INFN Sezione di Roma), Valerio Ippolito (INFN Sezione di Roma), Graziella Russo (Sapienza Universit\`a di Roma, INFN Sezione di Roma)

Graph Neural Network Acceleration on FPGAs for Fast Inference in Future Muon Triggers at HL-LHC
The High-Luminosity LHC (HL-LHC) will reach luminosities up to 7 times higher than the previous run, yielding denser events and larger occupancies. Next generation trigger algorithms must retain reliable selection within a strict latency budget. This work explores machine-learning approaches for future muon triggers, using the ATLAS Muon Spectrometer as a benchmark. A Convolutional Neural Network (CNN) is used as a reference, while a Graph Neural Network (GNN) is introduced as a natural model f…

Another big jump in atmospheric CO2 at Mauna Loa: based on daily values, the October average was ~425.0 ppm, that's 2.6 ppm higher than last year.
"US government is closed; site not updated", so we'll have to rely on the automated data collection for now.

OptimES: Optimizing Federated Learning Using Remote Embeddings for Graph Neural Networks
Pranjal Naman, Yogesh Simmhan
https://arxiv.org/abs/2509.22922 https://

OptimES: Optimizing Federated Learning Using Remote Embeddings for Graph Neural Networks
Graph Neural Networks (GNNs) have experienced rapid advancements in recent years due to their ability to learn meaningful representations from graph data structures. However, in most real-world settings, such as financial transaction networks and healthcare networks, this data is localized to different data owners and cannot be aggregated due to privacy concerns. Federated Learning (FL) has emerged as a viable machine learning approach for training a shared model that iteratively aggregates loc…

"[Scotland is] almost exactly as wealthy as the eurozone countries but we’re exporting wealth at twice the rate of even the most indebted poor countries. Can I get you to reflect on that – Scotland is rich like Europe but leaks wealth much, much worse than sub-Saharan Africa...
Since devolution, the cumulative total of the wealth we have exported is now well over £280 billion" -- Robin McAlpine

flickr_aminer: Flickr social graph
This network contains the social graph of flickr, a popular photo sharing network for users to upload photos and share photos, where a directed edge (i,j) means that user i follows user j.
This network has 214626 nodes and 9114557 edges.
Tags: Social, Online, Unweighted
https://

Items Proxy Bridging: Enabling Frictionless Critiquing in Knowledge Graph Recommendations
Huanyu Zhang, Xiaoxuan Shen, Yu Lei, Baolin Yi, Jianfang Liu, Yinao xie
https://arxiv.org/abs/2509.26107

Items Proxy Bridging: Enabling Frictionless Critiquing in Knowledge Graph Recommendations
Modern recommender systems place great inclination towards facilitating user experience, as more applications enabling users to critique and then refine recommendations immediately. Considering the real-time requirements, critique-able recommender systems typically straight modify the model parameters and update the recommend list through analyzing the user critiquing keyphrases in the inference phase. Current critiquing methods require first constructing a specially designated model which esta…

Left-lateralized reduced white matter structural connectivity in young women with obesity: analysis of graph theory applied to inter-tract correlation matrices
Jos\'e Gerardo Su\'arez-Garc\'ia, Eduardo Moreno-Barbosa, Javier M. Hern\'andez-L\'opez, Jorge Vel\'azquez-Castro, Benito de Celis-Alonso
https://arxiv.org/a…

Left-lateralized reduced white matter structural connectivity in young women with obesity: analysis of graph theory applied to inter-tract correlation matrices
Objective: Differences in WM structural connectivity were sought by comparing graph measures from young women with normal weight ($D_\mathrm{norm}$) and obesity ($D_\mathrm{over}$), studying FA-based inter-tract correlation matrices. Methods: Undirected binary adjacency matrices were created from WM inter-tract correlation matrices. Sixteen global graph measures were compared between the $D_\mathrm{norm}$ and $D_\mathrm{over}$ groups. At the nodal level, four graph measures were compared. Opt…

Faltings elliptic curves in twisted $\mathbb Q$-isogeny classes
Enrique Gonz\'alez-Jim\'enez, Joan-C. Lario
https://arxiv.org/abs/2509.23283 https://

Faltings elliptic curves in twisted $\mathbb Q$-isogeny classes
Let $G$ be the graph attached to the $\mathbb Q$-isogeny class of an elliptic curve defined over $\mathbb Q$: that is, a vertex for every elliptic curve defined over $\mathbb Q$ in the isogeny class, and edges in correspondence with the prime degree rational isogenies between them. Stevens shows that there is a unique elliptic curve in $G$ with minimal Faltings height. We call this curve the Faltings elliptic curve in $G$. For every square-free integer $d$, we consider the graph~$G^d$ attache…

Experimentally co-evolved E. coli and yeast achieve stable coexistence — and the coevolved E. coli, but not the yeast, is able to resist invasion by other bacterial strains
https://doi.org/10.1007/s00248-025-02618-w

Why there is no tsunami of waste #EV batteries. And look at the EV share in Ukraine 🇺🇦. Why it is important to get V2G/V2L working for older EVs right now.

Rebuild AC Power Flow Models with Graph Attention Networks
Yuting Hu, Jinjun Xiong
https://arxiv.org/abs/2509.22733 https://arxiv.org/pdf/2509.22733…

Rebuild AC Power Flow Models with Graph Attention Networks
A full power flow (PF) model is a complete representation of the physical power network. Traditional model-based methods rely on the full PF model to implement power flow analysis. In practice, however, some PF model parameters can be inaccurate or even unavailable due to the uncertainties or dynamics in the power systems. Moreover, because the power network keeps evolving with possibly changing topology, the generalizability of a PF model to different network sizes and typologies should be con…

New nonabelian Hodge graphs from twisted irregular connections
Jean Dou\c{c}ot
https://arxiv.org/abs/2509.24861 https://arxiv.org/pdf/2509.24861

New nonabelian Hodge graphs from twisted irregular connections
It is known that any meromorphic connection on the Riemann sphere determines a finite diagram encoding its global Cartan matrix, and that it is invariant under the Fourier-Laplace transform. If the connection is tame at finite distance and untwisted at infinity, the diagram is actually a graph, corresponding to a symmetric generalised Cartan matrix, and it was proved by Boalch/Hiroe-Yamakawa that the corresponding nonabelian Hodge moduli space contains the Nakajima quiver variety of the graph a…

NeuSO: Neural Optimizer for Subgraph Queries
Linglin Yang, Lei Zou, Chunshan Zhao
https://arxiv.org/abs/2509.23775 https://arxiv.org/pdf/2509.23775

NeuSO: Neural Optimizer for Subgraph Queries
Subgraph query is a critical task in graph analysis with a wide range of applications across various domains. Most existing methods rely on heuristic vertex matching orderings, which may significantly degrade enumeration performance for certain queries. While learning-based optimizers have recently gained attention in the context of relational databases, they cannot be directly applied to subgraph queries due to the heterogeneous and schema-flexible nature of graph data, as well as the large nu…

Flow polytopes for extensions of bipartite graphs
Benjamin Braun, Kaitlin Bruegge, Robert Davis, Derek Hanely
https://arxiv.org/abs/2509.26445 https://arxi…

Flow polytopes for extensions of bipartite graphs
The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the extension of $G$ and the almost-degree-whiskered graph of $G$. We prove that the normalized volume of the flow polytope for the extension of $G$ is equal to the number of matchings in the almost-degree-whiskered graph of $G$. Further, we refine this result by …

A Generative Model for Controllable Feature Heterophily in Graphs
Haoyu Wang, Renyuan Ma, Gonzalo Mateos, Luana Ruiz
https://arxiv.org/abs/2509.23230 https://

A Generative Model for Controllable Feature Heterophily in Graphs
We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of t…

as_skitter: Skitter IP graph (2005)
An aggregate snapshot of the Internet Protocol (IP) graph, as measured by the traceroute tool on CAIDA's skitter infrastructure, in 2005.
This network has 1696415 nodes and 11095298 edges.
Tags: Technological, Communication, Unweighted
https://networks.skewed.de/net/as_s…

Kinetic Monte Carlo prediction of the morphology of pentaerythritol tetranitrate
Jacob Jeffries, Himanshu Singh, Romain Perriot, Christian Negre, Antonio Redondo, Enrique Martinez
https://arxiv.org/abs/2509.25490

Kinetic Monte Carlo prediction of the morphology of pentaerythritol tetranitrate
In this work, we develop an atomistic, graph-based kinetic Monte Carlo (KMC) simulation routine to predict crystal morphology. Within this routine, we encode the state of the supercell in a binary occupation vector and the topology of the supercell in a simple nearest-neighbor graph. From this encoding, we efficiently compute the interaction energy of the system as a quadratic form of the binary occupation vector, representing pairwise interactions. This encoding, coupled with a simple diffusio…

Well-Quasi-Ordering Eulerian Digraphs Embeddable in Surfaces by Strong Immersion
Dario Cavallaro, Ken-ichi Kawarabayashi, Stephan Kreutzer
https://arxiv.org/abs/2509.26260 https…

Well-Quasi-Ordering Eulerian Digraphs Embeddable in Surfaces by Strong Immersion
We prove that for every surface $Σ$, the class of Eulerian directed graphs that are Eulerian embeddable into $Σ$ (in particular they have degree at most $4$) is well-quasi-ordered by strong immersion. This result marks one of the most versatile directed graph classes (besides tournaments) for which we are aware of a positive well-quasi-ordering result regarding a well-studied graph relation. Our result implies that the class of bipartite circle graphs is well-quasi-ordered under the pivot-m…

DFG-PCN: Point Cloud Completion with Degree-Flexible Point Graph
Zhenyu Shu, Jian Yao, Shiqing Xin
https://arxiv.org/abs/2509.23703 https://arxiv.org/pdf/2…

DFG-PCN: Point Cloud Completion with Degree-Flexible Point Graph
Point cloud completion is a vital task focused on reconstructing complete point clouds and addressing the incompleteness caused by occlusion and limited sensor resolution. Traditional methods relying on fixed local region partitioning, such as k-nearest neighbors, which fail to account for the highly uneven distribution of geometric complexity across different regions of a shape. This limitation leads to inefficient representation and suboptimal reconstruction, especially in areas with fine-gra…

Let the SwiftUI graph editing begin!

Symmetric monoidal extensions and graph cobordisms between finite sets
Andrea Bianchi
https://arxiv.org/abs/2509.22575 https://arxiv.org/pdf/2509.22575

Symmetric monoidal extensions and graph cobordisms between finite sets
Given a symmetric monoidal $(\infty,n)$-category $\mathcal{C}$ and a space $X$, we address the problem of explicitly describing the symmetric monoidal $(\infty,n)$-category freely obtained from $\mathcal{C}$ by adjoining $X$ new $n$-morphisms with prescribed sources and targets. We develop an apparatus of tools that allow one to detect in concrete situations such a free symmetric monoidal extension. As motivating application, we introduce a symmetric monoidal $(\infty,2)$-category ${\mathbb{G}\…

On random bipartite graphs evolving by degrees
Neeladri Maitra
https://arxiv.org/abs/2509.23943 https://arxiv.org/pdf/2509.23943

On random bipartite graphs evolving by degrees
In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $α$ and $β$. The graph evolves starting from $B_0$, the empty graph (with only isolated vertices). Given $B_t$, a non-adjacent vertex pair $u \in {L}, v \in {R}$ is sampled with probability proportional to $(d_u(t)+α)(d_v(t)+β)$, and the edge $\{u,v\}$ is included to $…

Here is an updated version of the #NFDI graph: large nodes are consortia, small nodes are institutions. Graph created with data from #Wikidata, visualized with #Gephi, using force atlas algorithm and modularity class c…

Hybrid Graph Embeddings and Louvain Algorithm for Unsupervised Community Detection
Dalila Khettaf, Djamel Djenouri, Zeinab Rezaeifar, Youcef Djenouri
https://arxiv.org/abs/2509.23411

Hybrid Graph Embeddings and Louvain Algorithm for Unsupervised Community Detection
This paper proposes a novel community detection method that integrates the Louvain algorithm with Graph Neural Networks (GNNs), enabling the discovery of communities without prior knowledge. Compared to most existing solutions, the proposed method does not require prior knowledge of the number of communities. It enhances the Louvain algorithm using node embeddings generated by a GNN to capture richer structural and feature information. Furthermore, it introduces a merging algorithm to refine th…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
James Bryden, Peter Rowley
https://arxiv.org/abs/2509.25901 https://arxiv.org/pdf/2509.25…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
Given a finite group $G$ and a conjugacy class of involutions $X$ of $G$, we define the commuting involution graph $\mathcal{C}(G,X)$ to be the graph with vertex set $X$ and $x,y \in X$ adjacent if and only if $x \neq y$ and $xy =yx$. In this paper the automorphism group of the graph $\mathcal{C}(G,X)$ is determined when $G = PSL_2(q)$.

On the Capacity of Self-Attention
Micah Adler
https://arxiv.org/abs/2509.22840 https://arxiv.org/pdf/2509.22840

On the Capacity of Self-Attention
While self-attention is known to learn relations among tokens, we lack a formal understanding of its capacity: how many distinct relations can a single layer reliably recover for a given budget? To formalize this, we introduce Relational Graph Recognition (RGR), where the key-query channel represents a graph on $m$ items with $m'$ directed edges, and, given a context of items, must recover the neighbors of each item. We measure resources by the total key dimension $D_K = h\,d_k$. Within this …

as_skitter: Skitter IP graph (2005)
An aggregate snapshot of the Internet Protocol (IP) graph, as measured by the traceroute tool on CAIDA's skitter infrastructure, in 2005.
This network has 1696415 nodes and 11095298 edges.
Tags: Technological, Communication, Unweighted
https://networks.skewed.de/net/as_s…

Graph Theory Meets Federated Learning over Satellite Constellations: Spanning Aggregations, Network Formation, and Performance Optimization
Fardis Nadimi, Payam Abdisarabshali, Jacob Chakareski, Nicholas Mastronarde, Seyyedali Hosseinalipour
https://arxiv.org/abs/2509.24932

Graph Theory Meets Federated Learning over Satellite Constellations: Spanning Aggregations, Network Formation, and Performance Optimization
We introduce Fed-Span, a novel federated/distributed learning framework designed for low Earth orbit satellite constellations. By leveraging graph-theoretic principles, Fed-Span addresses critical challenges inherent to distributed learning in dynamic satellite networks, including intermittent satellite connectivity, heterogeneous computational capabilities of satellites, and time-varying satellites' datasets. At its core, Fed-Span builds upon minimum spanning tree (MST) and minimum spanning fo…

myspace_aminer: MySpace social graph
This network contains the social graph of MySpace, a social networking website which also has a strong music emphasis. A directed edge (i,j) means that user i follows user j.
This network has 854498 nodes and 6489736 edges.
Tags: Social, Online, Unweighted
https://netwo…

On the Anti-Ramsey Number of Spanning Linear Forests with Paths of Lengths 2 and 3
Ali Ghalavand, Xueliang Li
https://arxiv.org/abs/2509.25949 https://arxi…

On the Anti-Ramsey Number of Spanning Linear Forests with Paths of Lengths 2 and 3
An edge-coloring of a graph $G$ assigns a color to each edge in the edge set $E(G)$. A graph $G$ is considered to be rainbow under an edge-coloring if all of its edges have different colors. For a positive integer $n$, the anti-Ramsey number of a graph $G$, denoted as $AR(n, G)$, represents the maximum number of colors that can be used in an edge-coloring of the complete graph $K_n$ without containing a rainbow copy of $G$. This concept was introduced by Erdős et al. in 1975. The anti-Ramsey n…

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Two classes of quantum spin systems that are gapped on any bounded-degree graph
Nicholas Hunter-Jones, Marius Lemm
https://arxiv.org/abs/2509.22438 https://

Two classes of quantum spin systems that are gapped on any bounded-degree graph
We study translation-invariant quantum spin Hamiltonians on general graphs with non-commuting interactions either given by (i) a random rank-$1$ projection or (ii) Haar projectors. For (i), we prove that the Hamiltonian is gapped on any bounded-degree graph with high probability at large local dimension. For (ii), we obtain a gap for sufficiently large local dimension. Our results provide examples where the folklore belief that typical translation-invariant Hamiltonians are gapped can be proved…

livejournal_aminer: Livejournal social graph
This network contains the social graph of Livejournal, a free on-line social network where users can keep a blog, journal or diary, where a directed edge (i,j) means that user i follows user j.
This network has 3017286 nodes and 87037567 edges.
Tags: Social, Online, Unweighted
https://…

Computing k-mers in Graphs
Jarno N. Alanko, Maximo Perez-Lopez
https://arxiv.org/abs/2509.22885 https://arxiv.org/pdf/2509.22885

Computing k-mers in Graphs
We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Siren, TCS 2017), we show that distinct $k$-mers of such a graph $W$ can be counted using $O(|W|k)$ or $O(n^4 \log k)$…

Model-Free Dynamic Consensus in Multi-Agent Systems: A Q-Function Perspective
Maryam Babazadeh, Naim Bajcinca
https://arxiv.org/abs/2509.24598 https://arxi…

Model-Free Dynamic Consensus in Multi-Agent Systems: A Q-Function Perspective
This paper presents a new method for achieving dynamic consensus in linear discrete-time homogeneous multi-agent systems (MAS) with marginally stable or unstable dynamics. The guarantee of consensus in this setting involves a set of constraints based on the graph's spectral properties, complicating the design of the coupling gains. This challenge intensifies for large-scale systems with diverse graph Laplacian spectra. The proposed approach reformulates the dynamic consensus problem with a pres…

TRACE: Learning to Compute on Graphs
Ziyang Zheng, Jiaying Zhu, Jingyi Zhou, Qiang Xu
https://arxiv.org/abs/2509.21886 https://arxiv.org/pdf/2509.21886

TRACE: Learning to Compute on Graphs
Learning to compute, the ability to model the functional behavior of a computational graph, is a fundamental challenge for graph representation learning. Yet, the dominant paradigm is architecturally mismatched for this task. This flawed assumption, central to mainstream message passing neural networks (MPNNs) and their conventional Transformer-based counterparts, prevents models from capturing the position-aware, hierarchical nature of computation. To resolve this, we introduce \textbf{TRACE},…

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Packing subgraphs in regular graphs
Shoham Letzter, Abhishek Methuku, Benny Sudakov
https://arxiv.org/abs/2509.26180 https://arxiv.org/pdf/2509.26180

Packing subgraphs in regular graphs
An $H$-packing in a graph $G$ is a collection of pairwise vertex-disjoint copies of $H$ in $G$. We prove that for every $c > 0$ and every bipartite graph $H$, any $\lfloor{cn}\rfloor$-regular graph $G$ admits an $H$-packing that covers all but a constant number of vertices. This resolves a problem posed by Kühn and Osthus in 2005. Moreover, our result is essentially tight: the conclusion fails if $G$ is not both regular and sufficiently dense; it is in general not possible to guarantee coverin…

Some bounds on the number of non isomorphic cyclic k-cycle systems of the complete graph
Lotrenzo Mella, Gloria Rinaldi
https://arxiv.org/abs/2509.24015 https://

Some bounds on the number of non isomorphic cyclic k-cycle systems of the complete graph
In a recent paper (2024) M. Buratti and M.E:Muzychuck have established some lower bounds on the number of non isomorphic cyclic Steiner Triple Systems of order $v\equiv 1$ (mod $6$). We complete their result to the case $v\equiv 3$ (mod $6$). For each odd $k > 3$ we also find lower bounds for the number of non isomorphic cyclic $k$-cycle systems of a complete graph.

Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models
Ehsan Sharifian, Saber Salehkaleybar, Negar Kiyavash
https://arxiv.org/abs/2509.21423 https://

Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models
We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each graph in an equivalence class corresponds to a perfect matching in a bipartite graph. This bipar…

Parallel Algorithms for the One Sided Crossing Minimization Problem
Bogdan-Ioan Popa, Adrian-Marius Dumitran, Livia Magureanu
https://arxiv.org/abs/2509.23706 https://

Parallel Algorithms for the One Sided Crossing Minimization Problem
The One Sided Crossing Minimization (OSCM) problem is an optimization problem in graph drawing that aims to minimize the number of edge crossings in bipartite graph layouts. It has practical applications in areas such as network visualization and VLSI (Very Large Scale Integration) design, where reducing edge crossings improves the arrangement of circuit components and their interconnections. Despite the rise of multi-core systems, the parallelization of exact and fixed-parameter tractable (FPT…

Learning the Neighborhood: Contrast-Free Multimodal Self-Supervised Molecular Graph Pretraining
Boshra Ariguib, Mathias Niepert, Andrei Manolache
https://arxiv.org/abs/2509.22468

Learning the Neighborhood: Contrast-Free Multimodal Self-Supervised Molecular Graph Pretraining
High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce. While self-supervised pretraining on molecular graphs has shown promise, many existing approaches either depend on hand-crafted augmentations or complex generative objectives, and often rely solely on 2D topology, leaving valuable 3D structural information underutilized. To address this gap, we introduce C-FREE (Contrast-Free Representation learning on Ego…

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

Diameter Bounds for Friends-and-Strangers Graphs
Amogh Akella, Rupert Li
https://arxiv.org/abs/2509.23511 https://arxiv.org/pdf/2509.23511

Diameter Bounds for Friends-and-Strangers Graphs
Consider two $n$-vertex graphs $X$ and $Y$, where we interpret $X$ as a social network with edges representing friendships and $Y$ as a movement graph with edges representing adjacent positions. The friends-and-strangers graph $\mathsf{FS}(X,Y)$ is a graph on the $n!$ permutations $V(X)\to V(Y)$, where two configurations are adjacent if and only if one can be obtained from the other by swapping two friends located on adjacent positions. Friends-and-strangers graphs were first introduced by De…

internet_as: Internet AS graph (2006)
A symmetrized snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from BGP tables posted by the University of Oregon Route Views Project. This snapshot was created on 22 July 2006.
This network has 22963 nodes and 48436 edges.
Tags: Technological, Communication, Unweighted

internet_as: Internet AS graph (2006)
A symmetrized snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from BGP tables posted by the University of Oregon Route Views Project. This snapshot was created on 22 July 2006.
This network has 22963 nodes and 48436 edges.
Tags: Technological, Communication, Unweighted

The existence of unexpected automorphisms in direct product graphs
Xiaomeng Wang, Yan-Li Qin, Binzhou Xia
https://arxiv.org/abs/2509.26170 https://arxiv.or…

The existence of unexpected automorphisms in direct product graphs
A pair of graphs $(Γ,Σ)$ is called unstable if their direct product $Γ\timesΣ$ admits automorphisms not from $\mathrm{Aut}(Γ)\times\mathrm{Aut}(Σ)$, and such automorphisms are said to be unexpected. The stability of a graph $Γ$ refers to that of $(Γ,K_2)$. While the stability of individual graphs has been relatively well studied, much less is known for graph pairs. In this paper, we propose a conjecture that provides the best possible reduction of the stability of a graph pair to the st…

trec_web: TREC WT10g (2003)
A web graph network originally constructed in 2003 as a testbed for information-retrieval techniques, including web search engines. Distributed by University of Glasgow.
This network has 1601787 nodes and 8063026 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net…

A $q$-analogue of distance matrix of bi-block graphs
Joyentanuj Das
https://arxiv.org/abs/2509.26060 https://arxiv.org/pdf/2509.26060

A $q$-analogue of distance matrix of bi-block graphs
A $q$-analogue of the distance matrix, referred to as the \emph{$q$-distance matrix}, is obtained from the distance matrix by replacing each nonzero entry $α$ with the sum $1+q+\cdots+q^{α-1}$. This notion was introduced independently by Bapat, Lal, and Pati~\cite{Ba-Lal-Pati}, and by Yan and Yeh~\cite{Yan}. A connected graph is called a \emph{bi-block graph} if each of its blocks is a complete bipartite graph. In this paper, we derive explicit formulas for the determinant and the inverse of …

stanford_web: Webgraph (Stanford)
The web graph of Stanford University (stanford.edu), as collected in 2002. Nodes represent pages and directed edges represent hyperlinks between them.
This network has 281904 nodes and 2312497 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/s…

berkstan_web: Webgraph (Berkeley-Stanford)
The web graph of Berkeley and Stanford Universities (berkeley.edu and stanford.edu), as collected in 2002. Nodes represent pages and directed edges represent hyperlinks between them.
This network has 685231 nodes and 7600595 edges.
Tags: Informational, Web graph, Unweighted
https://

lastfm_aminer: Last.fm social graph
This network contains the social graph of last.fm, a site that provides a streaming radio service, where users can search music and get personalized recommendation. A directed edge (i,j) means that user i follows user j.
This network has 136409 nodes and 1685524 edges.
Tags: Social, Online, Unweighted

Maximum Spread of Vertex Degrees in a Simple Graph
Sergey Dmitrievich Onishchenko
https://arxiv.org/abs/2509.21429 https://arxiv.org/pdf/2509.21429

Maximum Spread of Vertex Degrees in a Simple Graph
We consider the following problem: let $n>k$ be natural numbers, and let $G$ be a graph on $n$ vertices (undirected, without loops or multiple edges). Denote by $h_k(G)$ the number of unordered pairs of vertices in the graph $G$ whose degrees differ by less than $k$. We aim to determine the smallest possible value $f(n,k)$ of the quantity $h_k(G)$. Interest in this question is motivated by the fact that the bipartite analogue of the problem enabled S. Cichomski and F. Petrov to prove the Burdzy…

myspace_aminer: MySpace social graph
This network contains the social graph of MySpace, a social networking website which also has a strong music emphasis. A directed edge (i,j) means that user i follows user j.
This network has 854498 nodes and 6489736 edges.
Tags: Social, Online, Unweighted
https://netwo…

Ramsey numbers of long even cycles versus books
Qizhong Lin, Shixi Song
https://arxiv.org/abs/2509.26323 https://arxiv.org/pdf/2509.26323

Ramsey numbers of long even cycles versus books
For any positive integers $k$ and $n$, let $B_n^{(k)}$ be the book graph consisting of $n$ copies of the complete graph $K_{k+1}$ sharing a common $K_k$. Let $C_m$ be a cycle of length $m$. Prior work by Allen, Łuczak, Polcyn, and Zhang (2023) established the Ramsey number $R(C_{m},B_n^{(1)})$ for all sufficiently large even integer $m = Ω(n^{9/10})$. Recently, Hu, Lin, Łuczak, Ning, and Peng (2025) obtained the exact value of $R(C_{m},B_n^{(2)})$ under the same asymptotic conditions. A natu…

livejournal_aminer: Livejournal social graph
This network contains the social graph of Livejournal, a free on-line social network where users can keep a blog, journal or diary, where a directed edge (i,j) means that user i follows user j.
This network has 3017286 nodes and 87037567 edges.
Tags: Social, Online, Unweighted
https://

livejournal_aminer: Livejournal social graph
This network contains the social graph of Livejournal, a free on-line social network where users can keep a blog, journal or diary, where a directed edge (i,j) means that user i follows user j.
This network has 3017286 nodes and 87037567 edges.
Tags: Social, Online, Unweighted
https://

On Independent Spanning Trees in Random and Pseudorandom Graphs
Nemanja Dragani\'c, Keith Frankston, Michael Krivelevich, Alexey Pokrovskiy, Liana Yepremyan
https://arxiv.org/abs/2509.26401

On Independent Spanning Trees in Random and Pseudorandom Graphs
In 1989, Zehavi and Itai conjectured that every $k$-connected graph contains $k$ independent spanning trees rooted at any prescribed vertex $r$. That is, for each vertex $v$, the unique $r$-$v$ paths within these $k$ spanning trees are internally disjoint. This fundamental problem has received much attention, in part motivated by its applications to network reliability, but despite that has only been resolved for $k \le 4$ and certain restricted graph families. We establish the conjecture for…

Signless Laplacian characterization of cones over disjoint unions of cycles, edges and isolated vertices
Jiachang Ye, Jianguo Qian, Zoran Stanic
https://arxiv.org/abs/2509.25925

Signless Laplacian characterization of cones over disjoint unions of cycles, edges and isolated vertices
Two graphs are said to be $Q$-cospectral if they share the same signless Laplacian spectrum. A simple graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if there exists no other non-isomorphic simple graph with the same signless Laplacian spectrum. In this paper, we establish the following results: (1) Let$G \cong K_{1} \vee \bigl(C_{k} \cup qK_{2} \cup sK_{1}\bigr),$ with $q,s \geq 1$, $k \geq 4$, and at least $21$ vertices. If $k$ is odd, then $G$ is DQS.…

The typical algebraic shifting of a surface
Denys Bulavka, Eran Nevo, Yuval Peled
https://arxiv.org/abs/2509.26525 https://arxiv.org/pdf/2509.26525

The typical algebraic shifting of a surface
We initiate a statistical study of Kalai's exterior algebraic shifting, focusing on concentration phenomena for random triangulations of a fixed space. First, for a uniform $n$-vertex refinement of any given graph $G$, we show that asymptotically almost-surely (a.a.s.) its exterior algebraic shifting is an explicit shifted graph depending only on $n$ and the Betti numbers of $G$. Next, for any given compact connected Riemannian surface $S$, sample $n$ points independently at random according to…

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web

Edge inducibility via local directed graphs
Ting-Wei Chao, Asaf Cohen Antonir, Anqi Li, Hung-Hsun Hans Yu
https://arxiv.org/abs/2509.24064 https://arxiv.or…

Edge inducibility via local directed graphs
In this paper we introduce the edge inducibility problem. This is a common refinement of both the well known Kruskal--Katona theorem and the inducibility question introduced by Pippenger and Golumbic. Our first result is a hardness result. It shows that for any graph $G$, there is a related graph $G'$ whose edge inducibility determines the vertex inducibility of $G$. Moreover, we determine the edge inducibility of every $G$ with at most $4$ vertices, and make some progress on the cases $G=C_5…

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web<…

netscience: Scientific collaborations in network science (2006)
A coauthorship network among scientists working on network science, from 2006. This network is a one-mode projection from the bipartite graph of authors and their scientific publications.
This network has 1589 nodes and 2742 edges.
Tags: Social, Collaboration, Weighted, Projection

as_skitter: Skitter IP graph (2005)
An aggregate snapshot of the Internet Protocol (IP) graph, as measured by the traceroute tool on CAIDA's skitter infrastructure, in 2005.
This network has 1696415 nodes and 11095298 edges.
Tags: Technological, Communication, Unweighted
https://networks.skewed.de/net/as_s…

On the Precise Asymptotics of $ex(n,n,n,K_{2,t})$ for even $t$
Zilin Luo
https://arxiv.org/abs/2509.21756 https://arxiv.org/pdf/2509.21756

On the Precise Asymptotics of $ex(n,n,n,K_{2,t})$ for even $t$
Let $K_{2,t}$ denote the complete bipartite graph. For an integer $n\ge 1$, let $ex(n,n,n,K_{2,t})$ be the maximum number of edges in an $n\times n\times n$ tripartite graph (that is, a 3-partite graph with three parts each of size $n$) containing no copy of $K_{2,t}$. In this paper we prove that, for even $t\ge 2$, $$ ex(n,n,n,K_{2,t}) \ge \frac{3\sqrt{t-1}}{\sqrt{2}}\, n^{3/2} + o(n^{3/2}). $$ Combining our construction with earlier work of Tait and Timmons, we obtain $$ \lim\limits_{n\to\inf…

An exponential upper bound for induced Ramsey numbers
Lucas Arag\~ao, Marcelo Campos, Gabriel Dahia, Rafael Filipe, Jo\~ao Pedro Marciano
https://arxiv.org/abs/2509.22629 https:…

An exponential upper bound for induced Ramsey numbers
The induced Ramsey number $R_{\mathrm{ind}}(H; r)$ of a graph $H$ is the minimum number $N$ such that there exists a graph with $N$ vertices for which all $r$-colourings of its edges contain a monochromatic induced copy of $H$. Our main result is the existence of a constant $C > 0$ such that, for every graph $H$ on $k$ vertices, these numbers satisfy \begin{equation*} R_{\mathrm{ind}}(H; r) \le r^{C r k}. \end{equation*} When $r = 2$, this resolves a conjecture of Erdős from 1975. For $r > 2…

trec_web: TREC WT10g (2003)
A web graph network originally constructed in 2003 as a testbed for information-retrieval techniques, including web search engines. Distributed by University of Glasgow.
This network has 1601787 nodes and 8063026 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net…

flickr_aminer: Flickr social graph
This network contains the social graph of flickr, a popular photo sharing network for users to upload photos and share photos, where a directed edge (i,j) means that user i follows user j.
This network has 214626 nodes and 9114557 edges.
Tags: Social, Online, Unweighted
https://

lastfm_aminer: Last.fm social graph
This network contains the social graph of last.fm, a site that provides a streaming radio service, where users can search music and get personalized recommendation. A directed edge (i,j) means that user i follows user j.
This network has 136409 nodes and 1685524 edges.
Tags: Social, Online, Unweighted