Tootfinder

Vertex-transitive nut graph order-degree existence problem
Ivan Damnjanovi\'c
https://arxiv.org/abs/2507.02481 https://arxiv.org/…

Vertex-transitive nut graph order-degree existence problem
A nut graph is a nontrivial simple graph whose adjacency matrix has a simple eigenvalue zero such that the corresponding eigenvector has no zero entries. It is known that the order $n$ and degree $d$ of a vertex-transitive nut graph satisfy $4 \mid d$, $d \ge 4$, $2 \mid n$ and $n \ge d + 4$; or $d \equiv 2 \pmod 4$, $d \ge 6$, $4 \mid n$ and $n \ge d + 6$. Here, we prove that for each such $n$ and $d$, there exists a $d$-regular Cayley nut graph of order $n$. As a direct consequence, we obtain…

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

Fast variational knowledge graph embedding
Pulak Ranjan Giri, Mori Kurokawa, Kazuhiro Saito
https://arxiv.org/abs/2507.02472 https://…

Fast variational knowledge graph embedding
Embedding of a knowledge graph(KG) entities and relations in the form of vectors is an important aspect for the manipulation of the KG database for several downstream tasks, such as link prediction, knowledge graph completion, and recommendation. Because of the growing size of the knowledge graph databases, it has become a daunting task for the classical computer to train a model efficiently. Quantum computer can help speedup the embedding process of the KGs by encoding the entities into a vari…

Graph-Embedding Empowered Entity Retrieval
Emma J. Gerritse, Faegheh Hasibi, Arjen P. de Vries
https://arxiv.org/abs/2506.03895 https://

Graph-Embedding Empowered Entity Retrieval
In this research, we investigate methods for entity retrieval using graph embeddings. While various methods have been proposed over the years, most utilize a single graph embedding and entity linking approach. This hinders our understanding of how different graph embedding and entity linking methods impact entity retrieval. To address this gap, we investigate the effects of three different categories of graph embedding techniques and five different entity linking methods. We perform a reranking…

SVD-Based Graph Fractional Fourier Transform on Directed Graphs and Its Application
Lu Li, Haiye Huo
https://arxiv.org/abs/2506.03925 https://

SVD-Based Graph Fractional Fourier Transform on Directed Graphs and Its Application
Graph fractional Fourier transform (GFRFT) is an extension of graph Fourier transform (GFT) that provides an additional fractional analysis tool for graph signal processing (GSP) by generalizing temporal-vertex domain Fourier analysis to fractional orders. In recent years, a large number of studies on GFRFT based on undirected graphs have emerged, but there are very few studies on directed graphs. Therefore, in this paper, one of our main contributions is to introduce two novel GFRFTs defined o…

Okay, spent a little time with Python's Matplotlib to get this graph of miles biked so far this year...
At some point I should be able to pull the data from Run Gap's SQLite database to automate this more, and get more granular.
I still need to figure out how to space the bars and some other formatting stuff but it's a good start!
#python

Improving the average dilation of a metric graph by adding edges
Sariel Har-Peled, Eliot W. Robson
https://arxiv.org/abs/2506.04246 https://

Improving the average dilation of a metric graph by adding edges
For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to augment $G$ with $k$ additional edges to reduce the maximum dilation. In this note, we consider a variant of this problem where the goal is to reduce the average dilation for pairs of points in $G$. We provide an $O(k)$ approximation algorithm for this proble…

Unrolling Nonconvex Graph Total Variation for Image Denoising
Songlin Wei, Gene Cheung, Fei Chen, Ivan Selesnick
https://arxiv.org/abs/2506.02381 https://

Unrolling Nonconvex Graph Total Variation for Image Denoising
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable …

A Brain Graph Foundation Model: Pre-Training and Prompt-Tuning for Any Atlas and Disorder
Xinxu Wei, Kanhao Zhao, Yong Jiao, Lifang He, Yu Zhang
https://arxiv.org/abs/2506.02044

A Brain Graph Foundation Model: Pre-Training and Prompt-Tuning for Any Atlas and Disorder
As large language models (LLMs) continue to revolutionize AI research, there is a growing interest in building large-scale brain foundation models to advance neuroscience. While most existing brain foundation models are pre-trained on time-series signals or region-of-interest (ROI) features, we propose a novel graph-based pre-training paradigm for constructing a brain graph foundation model. In this paper, we introduce the Brain Graph Foundation Model, termed BrainGFM, a unified framework that …

DrKGC: Dynamic Subgraph Retrieval-Augmented LLMs for Knowledge Graph Completion across General and Biomedical Domains
Yongkang Xiao, Sinian Zhang, Yi Dai, Huixue Zhou, Jue Hou, Jie Ding, Rui Zhang
https://arxiv.org/abs/2506.00708

DrKGC: Dynamic Subgraph Retrieval-Augmented LLMs for Knowledge Graph Completion across General and Biomedical Domains
Knowledge graph completion (KGC) aims to predict missing triples in knowledge graphs (KGs) by leveraging existing triples and textual information. Recently, generative large language models (LLMs) have been increasingly employed for graph tasks. However, current approaches typically encode graph context in textual form, which fails to fully exploit the potential of LLMs for perceiving and reasoning about graph structures. To address this limitation, we propose DrKGC (Dynamic Subgraph Retrieval-…

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
Anders Karlsson, Kamila Kashaeva
https://arxiv.org/abs/2506.02340 https://

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
In this paper, we obtain an explicit formula for the heat kernel on the infinite Cayley graph of the modular group $\operatorname{PSL}_2\mathbb{Z}$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends the method of Chung--Yau in~\cite{MR1667452} by observing that the Cayley graph strongly and regularly covers a weighted infinite line. We solve the spectral problem on this line to obtain an integral expression for its heat kernel, and then lift this to the Cayle…

Esto se ve realmente interesante. Una herramienta que permite migrar cuentas entre activitypub y ATprotocol conservando publicaciones y seguidores. Y, según entiendo, también permite migrar entre plataformas del mismo protocolo. Habrš que ver qué tal va.
https://blog.anew.social/bounce-a-cros…

Speaker Diarization with Overlapping Community Detection Using Graph Attention Networks and Label Propagation Algorithm
Zhaoyang Li, Jie Wang, XiaoXiao Li, Wangjie Li, Longjie Luo, Lin Li, Qingyang Hong
https://arxiv.org/abs/2506.02610

Speaker Diarization with Overlapping Community Detection Using Graph Attention Networks and Label Propagation Algorithm
In speaker diarization, traditional clustering-based methods remain widely used in real-world applications. However, these methods struggle with the complex distribution of speaker embeddings and overlapping speech segments. To address these limitations, we propose an Overlapping Community Detection method based on Graph Attention networks and the Label Propagation Algorithm (OCDGALP). The proposed framework comprises two key components: (1) a graph attention network that refines speaker embedd…

Graph Neural Networks for Jamming Source Localization
Dania Herzalla, Willian T. Lunardi, Martin Andreoni
https://arxiv.org/abs/2506.03196 https://

Graph Neural Networks for Jamming Source Localization
Graph-based learning has emerged as a transformative approach for modeling complex relationships across diverse domains, yet its potential in wireless security remains largely unexplored. In this work, we introduce the first application of graph-based learning for jamming source localization, addressing the imminent threat of jamming attacks in wireless networks. Unlike geometric optimization techniques that struggle under environmental uncertainties and dense interference, we reformulate local…

RLHGNN: Reinforcement Learning-driven Heterogeneous Graph Neural Network for Next Activity Prediction in Business Processes
Jiaxing Wang, Yifeng Yu, Jiahan Song, Bin Cao, Jing Fan, Ji Zhang
https://arxiv.org/abs/2507.02690

RLHGNN: Reinforcement Learning-driven Heterogeneous Graph Neural Network for Next Activity Prediction in Business Processes
Next activity prediction represents a fundamental challenge for optimizing business processes in service-oriented architectures such as microservices environments, distributed enterprise systems, and cloud-native platforms, which enables proactive resource allocation and dynamic service composition. Despite the prevalence of sequence-based methods, these approaches fail to capture non-sequential relationships that arise from parallel executions and conditional dependencies. Even though graph-ba…

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…

This https://arxiv.org/abs/2505.21299 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Distinguishing Graphs and Cost Number using Automorphism Representations
A \textit{distinguishing coloring} of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A \textit{2-distinguishable graph} is a graph which can be distinguished using 2 colors. The \textit{cost} $ρ(G)$ of a 2-distinguishable graph is the smallest size of a color set of a distinguishing coloring of $G$. The \textit{determining number} of a graph, $Det(G)$, is the minimum number of nodes, which if fixed by a coloring, would ensure that the…

Hardware-Accelerated Algorithm for Complex Function Roots Density Graph Plotting
Ruibai Tang, Chengbin Quan
https://arxiv.org/abs/2507.02164 https://

Hardware-Accelerated Algorithm for Complex Function Roots Density Graph Plotting
Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph plotting by approximating functions with polynomials and solving their roots using single-shift QR iteration. By leveraging the Hessenberg structure of companion matrices and optimizing QR decomposition with Givens rotations, we design a pipelined FPGA archi…

NGAT: A Node-level Graph Attention Network for Long-term Stock Prediction
Yingjie Niu, Mingchuan Zhao, Valerio Poti, Ruihai Dong
https://arxiv.org/abs/2507.02018

NGAT: A Node-level Graph Attention Network for Long-term Stock Prediction
Graph representation learning methods have been widely adopted in financial applications to enhance company representations by leveraging inter-firm relationships. However, current approaches face three key challenges: (1) The advantages of relational information are obscured by limitations in downstream task designs; (2) Existing graph models specifically designed for stock prediction often suffer from excessive complexity and poor generalization; (3) Experience-based construction of corporate…

Topology-Aware Graph Neural Network-based State Estimation for PMU-Unobservable Power Systems
Shiva Moshtagh, Behrouz Azimian, Mohammad Golgol, Anamitra Pal
https://arxiv.org/abs/2506.03493

Topology-Aware Graph Neural Network-based State Estimation for PMU-Unobservable Power Systems
Traditional optimization-based techniques for time-synchronized state estimation (SE) often suffer from high online computational burden, limited phasor measurement unit (PMU) coverage, and presence of non-Gaussian measurement noise. Although conventional learning-based models have been developed to overcome these challenges, they are negatively impacted by topology changes and real-time data loss. This paper proposes a novel deep geometric learning approach based on graph neural networks (GNNs…

This https://arxiv.org/abs/2504.19583 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Graph-Based Spectral Decomposition for Parameter Coordination in Language Model Fine-Tuning
This paper proposes a parameter collaborative optimization algorithm for large language models, enhanced with graph spectral analysis. The goal is to improve both fine-tuning efficiency and structural awareness during training. In the proposed method, the parameters of a pre-trained language model are treated as nodes in a graph. A weighted graph is constructed, and Laplacian spectral decomposition is applied to enable frequency-domain modeling and structural representation of the parameter spa…

Gromov-Wasserstein Bound between Reeb and Mapper Graphs
Ziyad Oulhaj, Mathieu Carri\`ere, Bertrand Michel
https://arxiv.org/abs/2506.02810 https://

Gromov-Wasserstein Bound between Reeb and Mapper Graphs
Since its introduction as a computable approximation of the Reeb graph, the Mapper graph has become one of the most popular tools from topological data analysis for performing data visualization and inference. However, finding an appropriate metric (that is, a tractable metric with theoretical guarantees) for comparing Reeb and Mapper graphs, in order to, e.g., quantify the rate of convergence of the Mapper graph to the Reeb graph, is a difficult problem. While several metrics have been propose…

Tipp: trackingfreies detailreiches und zuverlässiges Wetter gibt es nicht nur für #burgos über https://www.yr.no/en/forecast/graph/2-3127461/Spain…

Graph for Burgos
Weather forecast for Burgos for the next 3 days in a graph.

This https://arxiv.org/abs/2506.00261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

GPR: Empowering Generation with Graph-Pretrained Retriever
Graph retrieval-augmented generation (GRAG) places high demands on graph-specific retrievers. However, existing retrievers often rely on language models pretrained on plain text, limiting their effectiveness due to domain misalignment and structure ignorance. To address these challenges, we propose GPR, a graph-based retriever pretrained directly on knowledge graphs. GPR aligns natural language questions with relevant subgraphs through LLM-guided graph augmentation and employs a structure-aware…

This https://arxiv.org/abs/2501.10745 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Changing the ranking in eigenvector centrality of a weighted graph by small perturbations
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph ${\mathcal G}$ (both directed and undirected), we consider the associated weighted adjacency matrix $A$, which by definition is a non-negative matrix. The eigenvector centralities of the nodes of ${\mathcal G}$ are the entries of the Perron eigenvector of $A$, which is the (positive) eigenvector associated with the e…

r-graph-gallery.com provides example code for a variety of chart types, both in base R and ggplot: #rstats

This https://arxiv.org/abs/2505.00393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDB_…

S3AND: Efficient Subgraph Similarity Search Under Aggregated Neighbor Difference Semantics (Technical Report)
For the past decades, the \textit{subgraph similarity search} over a large-scale data graph has become increasingly important and crucial in many real-world applications, such as social network analysis, bioinformatics network analytics, knowledge graph discovery, and many others. While previous works on subgraph similarity search used various graph similarity metrics such as the graph isomorphism, graph edit distance, and so on, in this paper, we propose a novel problem, namely \textit{subgrap…

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://…

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.

This https://arxiv.org/abs/2505.19945 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Signed Angle Rigid Graphs for Network Localization and Formation Control
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation control. In recent years, the traditional rigidity theory has been extended by considering new types of local constraints such as bearing, angle, ratio of distance, etc. Among them, the signed angle constraint received extensive attention since it is practic…

DRAG: Distilling RAG for SLMs from LLMs to Transfer Knowledge and Mitigate Hallucination via Evidence and Graph-based Distillation
Jennifer Chen, Aidar Myrzakhan, Yaxin Luo, Hassaan Muhammad Khan, Sondos Mahmoud Bsharat, Zhiqiang Shen
https://arxiv.org/abs/2506.01954

DRAG: Distilling RAG for SLMs from LLMs to Transfer Knowledge and Mitigate Hallucination via Evidence and Graph-based Distillation
Retrieval-Augmented Generation (RAG) methods have proven highly effective for tasks requiring factual consistency and robust knowledge retrieval. However, large-scale RAG systems consume significant computational resources and are prone to generating hallucinated content from Humans. In this work, we introduce $\texttt{DRAG}$, a novel framework for distilling RAG knowledge from large-scale Language Models (LLMs) into small LMs (SLMs). Our approach leverages evidence- and knowledge graph-based d…

«But I think the core of what pisses me off is that selling this magic machine requires selling the idea that doing things is worthless. Because if doing something has some value, then it must be somehow better than pushing a button and receiving Whatever for essentially no cost. If you’re some assclown like Sam Altman, whose graph-go-up depends on convincing you to replace all your employees with ChatGPT, you have to destroy that idea.»
https://eev.ee/blog/2025/07/03/the-rise-of-whatever/
/HT @…

The Local Structure Theorem for Graph Minors with Finite Index
Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos, Sebastian Wiederrecht
https://arxiv.org/abs/2507.02769

The Local Structure Theorem for Graph Minors with Finite Index
The Local Structure Theorem (LST) for graph minors roughly states that every $H$-minor free graph $G$ that contains a sufficiently large wall $W$, there is a set of few vertices $A$ such that, upon removing $A$, the resulting graph $G':=G - A$ admits an "almost embedding" $δ$ into a surface $Σ$ in which $H$ does not embed. By almost embedding, we mean that there exists a hypergraph $\mathcal{H}$ whose vertex set is a subset of the vertex set of $G$ and an embedding of $\mathcal{H}$ in $Σ$ su…

Reweighted Spectral Partitioning Works: Bounds for Special Graph Classes
Jack Spalding-Jamieson
https://arxiv.org/abs/2506.01228 https://

Reweighted Spectral Partitioning Works: Bounds for Special Graph Classes
Spectral partitioning is a method that can be used to compute small sparse cuts or small edge-separators in a wide variety of graph classes, by computing the second-smallest eigenvalue (and eigenvector) of the Laplacian matrix. Upper bounds on this eigenvalue for certain graph classes imply that the method obtains small edge-separators for these classes, usually with a sub-optimal dependence on the maximum degree. In this work, we show that a related method, called reweighted spectral partition…

Oh yes... not one, but two #Mordor towers in the usage graphs. Can somebody please throw that #AI ring in Mount Doom?

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…

This https://arxiv.org/abs/2505.20089 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

Homophily Enhanced Graph Domain Adaptation
Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. In this paper, we highlight the significance of graph homophily, a pivotal factor for graph domain alignment, which, however, has long been overlooked in existing approaches. Specifically, our analysis first reveals that homophily discrepancies exist in benchmarks. Moreover, we also show that homophily discrepancies degrade GDA performance from bot…

Imitation and Heterogeneity Shape the Resilience of Community Currency Networks
Camilla Ancona, Dora Ricci, Carmela Bernardo, Francesco Lo Iudice, Anton Proskurnikov, Francesco Vasca
https://arxiv.org/abs/2507.02678

Imitation and Heterogeneity Shape the Resilience of Community Currency Networks
Community currency networks are made up of individuals and or companies that share some physical or social characteristics and engage in economic transactions using a virtual currency. This paper investigates the structural and dynamic properties of such mutual credit systems through a case study of Sardex, a community currency initiated and mainly operating in Sardinia, Italy. The transaction network is modeled as a directed weighted graph and analyzed through a graph theoretic framework focus…

❓ Wusstet ihr, dass ihr Metadaten in den Culture Knowledge Graph aufnehmen könnt?
💡 Eine kürzlich erschienene Guideline beschreibt mögliche Integrationswege und bietet grundlegende Hinweise zum Verständnis des Culture Knowledge Graphs.
➡️ Ihr findet die Handreichung in der deutschen und englischen Version auf unserer Knowledge Base:

This https://arxiv.org/abs/2412.11369 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

PSGraph: Differentially Private Streaming Graph Synthesis by Considering Temporal Dynamics
Streaming graphs are ubiquitous in daily life, such as evolving social networks and dynamic communication systems. Due to the sensitive information contained in the graph, directly sharing the streaming graphs poses significant privacy risks. Differential privacy, offering strict theoretical guarantees, has emerged as a standard approach for private graph data synthesis. However, existing methods predominantly focus on static graph publishing, neglecting the intrinsic relationship between adjac…

A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks
Xingchao Jian, Martin G\"olz, Feng Ji, Wee Peng Tay, Abdelhak M. Zoubir
https://arxiv.org/abs/2506.03496

A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks
We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make decisions for all hypotheses simultaneously, using all available $p$-values. In practice, this problem resembles the detection problem over a sensor network during a period of time. To solve this problem, we extend the traditional two-groups model such that …

Joint Power Control and Precoding for Cell-Free Massive MIMO Systems With Sparse Multi-Dimensional Graph Neural Networks
Yukun Ma, Jiayi Zhang, Ziheng Liu, Guowei Shi, Bo Ai
https://arxiv.org/abs/2507.01876

Joint Power Control and Precoding for Cell-Free Massive MIMO Systems With Sparse Multi-Dimensional Graph Neural Networks
Cell-free massive multiple-input multiple-output (CF mMIMO) has emerged as a prominent candidate for future networks due to its ability to significantly enhance spectral efficiency by eliminating inter-cell interference. However, its practical deployment faces considerable challenges, such as high computational complexity and the optimization of its complex processing. To address these challenges, this correspondence proposes a framework based on a sparse multi-dimensional graph neural network …

Ce graphe dit tout...
This graph says it all...
Source (in French but nicely illustrated) https://www.lemonde.fr/les-decodeurs/visuel/2025/07/02/comprendre-le-rechauffement-climatiq…

Comprendre le réchauffement climatique : comment nous avons bouleversé la planète
Deux siècles ont suffi à l’humanité pour dérégler le climat et enclencher une hausse des températures aux effets potentiellement dramatiques. Dans ce format visuel, « Le Monde » retrace cette évolution et les mécanismes à l’œuvre dans ce bouleversement.

This https://arxiv.org/abs/2209.12996 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
In this paper we study various rigidity aspects of the von Neumann algebra $L(Γ)$ where $Γ$ is a graph product group \cite{Gr90} whose underlying graph is a certain cycle of cliques and the vertex groups are the wreath-like product property (T) groups introduced recently in \cite{CIOS21}. Using an approach that combines methods from Popa's deformation/rigidity theory with new techniques pertaining to graph product algebras, we describe all symmetries of these von Neumann algebras and reduced …

This https://arxiv.org/abs/2502.09304 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

KET-RAG: A Cost-Efficient Multi-Granular Indexing Framework for Graph-RAG
Graph-RAG constructs a knowledge graph from text chunks to improve retrieval in Large Language Model (LLM)-based question answering. It is particularly useful in domains such as biomedicine, law, and political science, where retrieval often requires multi-hop reasoning over proprietary documents. Some existing Graph-RAG systems construct KNN graphs based on text chunk relevance, but this coarse-grained approach fails to capture entity relationships within texts, leading to sub-par retrieval and…

This https://arxiv.org/abs/2310.00940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

1-planar unit distance graphs
A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on $n$ vertices can have at most $\lfloor 3n - \sqrt{12n - 3}\rfloor$ edges. Recently, his conjecture was settled by Lavollée and Swanepoel. In this paper we consider $1$-planar unit distance graphs. We say that a graph is a $1$-planar unit distance graph if it can be drawn in the plane such that all edges are drawn as unit…

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung
https://arxiv.org/abs/2506.01826

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method t…

This https://arxiv.org/abs/2504.05424 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

Speculative Automated Refactoring of Imperative Deep Learning Programs to Graph Execution
Efficiency is essential to support ever-growing datasets, especially for Deep Learning (DL) systems. DL frameworks have traditionally embraced deferred execution-style DL code -- supporting symbolic, graph-based Deep Neural Network (DNN) computation. While scalable, such development is error-prone, non-intuitive, and difficult to debug. Consequently, more natural, imperative DL frameworks encouraging eager execution have emerged but at the expense of run-time performance. Though hybrid approach…

This https://arxiv.org/abs/2505.24226 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

E^2GraphRAG: Streamlining Graph-based RAG for High Efficiency and Effectiveness
Graph-based RAG methods like GraphRAG have shown promising global understanding of the knowledge base by constructing hierarchical entity graphs. However, they often suffer from inefficiency and rely on manually pre-defined query modes, limiting practical use. In this paper, we propose E^2GraphRAG, a streamlined graph-based RAG framework that improves both Efficiency and Effectiveness. During the indexing stage, E^2GraphRAG constructs a summary tree with large language models and an entity grap…

This https://arxiv.org/abs/2505.23240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Joint estimation of smooth graph signals from partial linear measurements
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the vertices, our goal is to estimate $x_t$'s. Assuming that the signals are smooth w.r.t $G$, in the sense that the quadratic variation of the signals over the graph is small, we obtain non-asymptotic bounds on the mean squared error for jointly recovering $x_t$'s, fo…

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…

Enhancing Power Flow Estimation with Topology-Aware Gated Graph Neural Networks
Shrenik Jadhav, Birva Sevak, Srijita Das, Wencong Su, Van-Hai Bui
https://arxiv.org/abs/2507.02078 …

Enhancing Power Flow Estimation with Topology-Aware Gated Graph Neural Networks
Accurate and scalable surrogate models for AC power flow are essential for real-time grid monitoring, contingency analysis, and decision support in increasingly dynamic and inverter-dominated power systems. However, most existing surrogates fall short of practical deployment due to their limited capacity to capture long-range nonlinear dependencies in meshed transmission networks and their weak enforcement of physical laws. These models often require extensive hyperparameter tuning, exhibit poo…

Zero-Knowledge Verifiable Graph Query Evaluation via Expansion-Centric Operator Decomposition
Hao Wu, Changzheng Wei, Yanhao Wang, Li Lin, Yilong Leng, Shiyu He, Minghao Zhao, Hanghang Wu, Ying Yan, Aoying Zhou
https://arxiv.org/abs/2507.00427

Zero-Knowledge Verifiable Graph Query Evaluation via Expansion-Centric Operator Decomposition
This paper investigates the feasibility of achieving zero-knowledge verifiability for graph databases, enabling database owners to cryptographically prove the query execution correctness without disclosing the underlying data. Although similar capabilities have been explored for relational databases, their implementation for graph databases presents unique challenges. This is mainly attributed to the relatively large complexity of queries in graph databases. When translating graph queries into …

A note on maximal plane subgraphs of the complete twisted graph containing perfect matchings
Elsa Oma\~na-Pulido, Eduardo Rivera-Campo
https://arxiv.org/abs/2507.02711

A note on maximal plane subgraphs of the complete twisted graph containing perfect matchings
The twisted graph $T_{n}$ is a drawing of the complete graph with $n$ vertices $v_{1},v_{2},\ldots ,v_{n}$ in which two edges $v_{i}v_{j}$ ($i

Rumors on evolving graphs through stationary times
Vicenzo Bonasorte
https://arxiv.org/abs/2506.04386 https://arxiv.org/pdf/2506.0438…

Rumors on evolving graphs through stationary times
We study rumor spreading in dynamic random graphs. Starting with a single informed vertex, the information flows until it reaches all the vertices of the graph (completion), according to the following process. At each step $k$, the information is propagated to neighbors of the informed vertices, in the $k$-th generated random graph. The way this information propagates from vertex to vertex at each step will depend on the ``protocol". We provide a method based on strong stationary times to study…

This https://arxiv.org/abs/2505.12910 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

SourceDetMamba: A Graph-aware State Space Model for Source Detection in Sequential Hypergraphs
Source detection on graphs has demonstrated high efficacy in identifying rumor origins. Despite advances in machine learning-based methods, many fail to capture intrinsic dynamics of rumor propagation. In this work, we present SourceDetMamba: A Graph-aware State Space Model for Source Detection in Sequential Hypergraphs, which harnesses the recent success of the state space model Mamba, known for its superior global modeling capabilities and computational efficiency, to address this challenge. …

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💡 Eine kürzlich erschienene Guideline beschreibt mögliche Integrationswege und bietet grundlegende Hinweise zum Verständnis des Culture Knowledge Graphs.
➡️ Ihr findet die Handreichung in der deutschen und englischen Version auf unserer Knowledge Base:

Quantum-like states from classical systems
Gregory D. Scholes
https://arxiv.org/abs/2507.00967 https://arxiv.org/pdf/2507.00967

Quantum-like states from classical systems
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space that comprises superpositions of states in a tensor product basis. The basis for constructing QL graphs and their properties is reviewed and extended. An optimization of the graph product is developed to produce a more compact graph with the essential proper…

A Generative Adaptive Replay Continual Learning Model for Temporal Knowledge Graph Reasoning
Zhiyu Zhang, Wei Chen, Youfang Lin, Huaiyu Wan
https://arxiv.org/abs/2506.04083

A Generative Adaptive Replay Continual Learning Model for Temporal Knowledge Graph Reasoning
Recent Continual Learning (CL)-based Temporal Knowledge Graph Reasoning (TKGR) methods focus on significantly reducing computational cost and mitigating catastrophic forgetting caused by fine-tuning models with new data. However, existing CL-based TKGR methods still face two key limitations: (1) They usually one-sidedly reorganize individual historical facts, while overlooking the historical context essential for accurately understanding the historical semantics of these facts; (2) They preserv…

On the proofs of Leighton's Graph Covering Theorem and a notion dual to commensurability
Nicholas Touikan
https://arxiv.org/abs/2507.01839 https://

On the proofs of Leighton's Graph Covering Theorem and a notion dual to commensurability
Leighton's Graph Covering Theorem states that if two finite graphs have the same universal covering tree, then they also have a common finite degree cover. Bass and Kulkarni gave an alternative proof of this fact using tree lattices. We give an example of two graphs that admit a common finite cover which can not be obtained using tree lattice techniques. The argument naturally leads to the question of when a commensuration can be induced by an embedding into a common finite index overgroup. We …

Not every graph can be reconstructed from its boundary distance matrix
Jos\'e C\'aceres, Ignacio M. Pelayo
https://arxiv.org/abs/2506.02652 https:/…

Not every graph can be reconstructed from its boundary distance matrix
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary vertices. The boundary distance matrix $\hat{D}_G$ of a graph $G=([n],E)$ is the square matrix of order $κ$, being $κ$ the order of $\partial(G)$, such that for every $i,j\in \partial(G)$, $[\hat{D}_G]_{ij}=d_G(i,j)$. In a recent paper [doi.org/10.7151/dmgt…

Marcello's completion of graphs
Johan Kok
https://arxiv.org/abs/2507.02015 https://arxiv.org/pdf/2507.02015

Marcello's completion of graphs
This paper initiates a study on a new optimization problem with regards to graph completion. The defined procedure is called, \emph{Marcello's completion} of a graph. For graph $G$ of order $n$ the \emph{Marcello number} is obtained by iteratively constructing graphs, $G_1,G_2,\dots,G_k$ by adding a maximal number of edges between pairs of distinct, non-adjacent vertices in accordance with the \emph{Marcello rule}. If for smallest $k$ the resultant graph $G_k \cong K_n$ then the Marcello number…

GPR: Empowering Generation with Graph-Pretrained Retriever
Xiaochen Wang, Zongyu Wu, Yuan Zhong, Xiang Zhang, Suhang Wang, Fenglong Ma
https://arxiv.org/abs/2506.00261

GPR: Empowering Generation with Graph-Pretrained Retriever
Graph retrieval-augmented generation (GRAG) places high demands on graph-specific retrievers. However, existing retrievers often rely on language models pretrained on plain text, limiting their effectiveness due to domain misalignment and structure ignorance. To address these challenges, we propose GPR, a graph-based retriever pretrained directly on knowledge graphs. GPR aligns natural language questions with relevant subgraphs through LLM-guided graph augmentation and employs a structure-aware…

Tunnelling Through Time Series: A Probabilistic Visibility Graph for Local and Global Pattern Discovery
Roberto Sotero, Jose Sanchez-Bornot
https://arxiv.org/abs/2507.01247

Tunnelling Through Time Series: A Probabilistic Visibility Graph for Local and Global Pattern Discovery
The growing availability of high-resolution, long-term time series data has highlighted the need for methods capable of capturing both local and global patterns. To address this, we introduce the Probabilistic Visibility Graph (PVG), a novel approach inspired by the quantum tunnelling phenomenon. The PVG extends the classical Visibility Graph (VG) by introducing probabilistic connections between time points that are obstructed in the VG due to intermediate values. We demonstrate the PVG's effec…

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
Jakub {\L}\k{a}cki, Slobodan Mitrovi\'c, Srikkanth Ramachandran, Wen-Horng Sheu
https://arxiv.org/abs/2506.04524

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition. We give a $(1+ε)$ approximate algorithm for the problem, which runs in $\tilde{O}(\sqrt{\log λ})$ MPC rounds, using sublinear space per machine and $\tilde{O}(λn)$ total space, where $λ$ is the arboricity of the input graph. Our result is obtained by pro…

Generating Large Semi-Synthetic Graphs of Any Size
Rodrigo Tuna, Carlos Soares
https://arxiv.org/abs/2507.02166 https://arxiv.org/pdf…

Generating Large Semi-Synthetic Graphs of Any Size
Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning, particularly with Graph Neural Networks, have enabled data-driven methods to learn and generate graphs without relying on predefined structural properties. Despite these advances, current models are limited by their reliance on node IDs, which restricts thei…

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
Ran An, Hengzhe Li, Jianbing Liu, Gaoxing Sun
https://arxiv.org/abs/2507.02277 https…

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
In 2018, Dankelmann, Gao, and Surmacs [J. Graph Theory, 88(1): 5--17, 2018] established sharp bounds on the oriented diameter of a bridgeless undirected graph and a bridgeless undirected bipartite graph in terms of vertex degree. In this paper, we extend these results to \emph{mixed graphs}, which contain both directed and undirected edges. Let the \emph{undirected degree} $d^*_G(x)$ of a vertex $x \in V(G)$ be the number of its incident undirected edges in a mixed graph $G$ of order $n$, and…

This https://arxiv.org/abs/2505.24434 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fields
Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To …

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Haiquan Zhao, Chengjin Li
https://arxiv.org/abs/2506.00403 https://

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks. The existing work has completed the steady state error analysis of the GSP LMS algorithm and GSP RLS algorithm in Gaussian noise scenarios, and a range of values for the step size of the GSP LMS algorithm has also been given. Meanwhile, the transient error a…

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

This https://arxiv.org/abs/2502.09891 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

ArchRAG: Attributed Community-based Hierarchical Retrieval-Augmented Generation
Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs) for solving question-answer (QA) tasks. The state-of-the-art RAG approaches often use the graph data as the external data since they capture the rich semantic information and link relationships between entities. However, existing graph-based RAG approaches cannot accurately identify the relevant information from the graph and also consume large numbers of tokens in the o…

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

Graph Contrastive Learning for Optimizing Sparse Data in Recommender Systems with LightGCL
Aravinda Jatavallabha, Prabhanjan Bharadwaj, Ashish Chander
https://arxiv.org/abs/2506.00048

Graph Contrastive Learning for Optimizing Sparse Data in Recommender Systems with LightGCL
Graph Neural Networks (GNNs) are powerful tools for recommendation systems, but they often struggle under data sparsity and noise. To address these issues, we implemented LightGCL, a graph contrastive learning model that uses Singular Value Decomposition (SVD) for robust graph augmentation, preserving semantic integrity without relying on stochastic or heuristic perturbations. LightGCL enables structural refinement and captures global collaborative signals, achieving significant gains over stat…

This https://arxiv.org/abs/2506.00689 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mutual-visibility of the disjointness graph of segments in ${\mathbb R}^2$
Let $G=(V(G),E(G))$ be a simple graph, and let $U\subseteq V(G)$. Two distinct vertices $x,y\in U$ are $U$-mutually visible if $G$ contains a shortest $x$-$y$ path that is internally disjoint from $U$. $U$ is called a mutual-visibility set of $G$ if any two vertices of $U$ are $U$-mutually visible. The mutual-visibility number $μ(G)$ of $G$ is the size of a largest mutual-visibility set of $G$. Let $P$ be a set of $n\geq 3$ points in ${\mathbb R}^2$ in general position. The disjointness graph …

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition
Anders Aamand, Justin Y. Chen, Mina Dalirrooyfard, Slobodan Mitrovi\'c, Yuriy Nevmyvaka, Sandeep Silwal, Yinzhan Xu
https://arxiv.org/abs/2507.01873

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition
We study differentially private algorithms for graph cut sparsification, a fundamental problem in algorithms, privacy, and machine learning. While significant progress has been made, the best-known private and efficient cut sparsifiers on $n$-node graphs approximate each cut within $\widetilde{O}(n^{1.5})$ additive error and $1+γ$ multiplicative error for any $γ> 0$ [Gupta, Roth, Ullman TCC'12]. In contrast, "inefficient" algorithms, i.e., those requiring exponential time, can achieve an $\wi…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Perfect $1$-factorisations of $K_{11,11}$
Jack Allsop, Ian M. Wanless
https://arxiv.org/abs/2506.02455 https://arxiv.org/pdf/2506.024…

Perfect $1$-factorisations of $K_{11,11}$
A perfect $1$-factorisation of a graph is a decomposition of that graph into $1$-factors such that the union of any two $1$-factors is a Hamiltonian cycle. A Latin square of order $n$ is row-Hamiltonian if for every pair $(r,s)$ of distinct rows, the permutation mapping $r$ to $s$ has a single cycle of length $n$. We report the results of a computer enumeration of the perfect $1$-factorisations of the complete bipartite graph $K_{11,11}$. This also allows us to find all row-Hamiltonian Latin sq…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Strongly regular and strongly walk-regular graphs that admit perfect state transfer
Sho Kubota, Hiroto Sekido, Harunobu Yata, Kiyoto Yoshino
https://arxiv.org/abs/2506.02530

Strongly regular and strongly walk-regular graphs that admit perfect state transfer
We study perfect state transfer in Grover walks on two important classes of graphs: strongly regular graphs and strongly walk-regular graphs. The latter class is a generalization of the former. We first give a complete classification of strongly regular graphs that admit perfect state transfer. The only such graphs are the complete bipartite graph $K_{2,2}$ and the complete tripartite graph $K_{2,2,2}$. We then show that, if a genuine strongly walk-regular graph admits perfect state transfer, t…

Combining social relations and interaction data in Recommender System with Graph Convolution Collaborative Filtering
Tin T. Tran, Vaclav Snasel, Loc Tan Nguyen
https://arxiv.org/abs/2506.02834

Combining social relations and interaction data in Recommender System with Graph Convolution Collaborative Filtering
A recommender system is an important subject in the field of data mining, where the item rating information from users is exploited and processed to make suitable recommendations with all other users. The recommender system creates convenience for e-commerce users and stimulates the consumption of items that are suitable for users. In addition to e-commerce, a recommender system is also used to provide recommendations on books to read, movies to watch, courses to take or websites to visit. Simi…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Learning Binarized Representations with Pseudo-positive Sample Enhancement for Efficient Graph Collaborative Filtering
Yankai Chen, Yue Que, Xinni Zhang, Chen Ma, Irwin King
https://arxiv.org/abs/2506.02750

Learning Binarized Representations with Pseudo-positive Sample Enhancement for Efficient Graph Collaborative Filtering
Learning vectorized embeddings is fundamental to many recommender systems for user-item matching. To enable efficient online inference, representation binarization, which embeds latent features into compact binary sequences, has recently shown significant promise in optimizing both memory usage and computational overhead. However, existing approaches primarily focus on numerical quantization, neglecting the associated information loss, which often results in noticeable performance degradation. …

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

This https://arxiv.org/abs/2503.06474 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

ROGRAG: A Robustly Optimized GraphRAG Framework
Large language models (LLMs) commonly struggle with specialized or emerging topics which are rarely seen in the training corpus. Graph-based retrieval-augmented generation (GraphRAG) addresses this by structuring domain knowledge as a graph for dynamic retrieval. However, existing pipelines involve complex engineering workflows, making it difficult to isolate the impact of individual components. It is also challenging to evaluate the retrieval effectiveness due to the overlap between the pretra…

Even-degeneracy of a random graph
Ting-Wei Chao, Dingding Dong, Zixuan Xu
https://arxiv.org/abs/2506.01021 https://arxiv.org/pdf/2506…

Even-degeneracy of a random graph
A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erdős--Renyi random graph $G(n,1/2)$ is even-degenerate with high probability, and asked whether an analogous result holds for any general $G(n,p)$. In this paper, we answer this question for any constant $p\in (0,1)$ in affirmation by proving that $G(n,p)$ is even-degenerate with high probability.

The Cycle Counts of Graphs
Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori, Thomas Zaslavsky
https://arxiv.org/abs/2507.02260 https://

The Cycle Counts of Graphs
We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the sole additional exception 13.

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…

Mutual-visibility of the disjointness graph of segments in ${\mathbb R}^2$
J. Lea\~nos, M. Lomel\'i-Haro, Christophe Ndjatchi, L. M. R\'ios-Castro
https://arxiv.org/abs/2506.00689

Mutual-visibility of the disjointness graph of segments in ${\mathbb R}^2$
Let $G=(V(G),E(G))$ be a simple graph, and let $U\subseteq V(G)$. Two distinct vertices $x,y\in U$ are $U$-mutually visible if $G$ contains a shortest $x$-$y$ path that is internally disjoint from $U$. $U$ is called a mutual-visibility set of $G$ if any two vertices of $U$ are $U$-mutually visible. The mutual-visibility number $μ(G)$ of $G$ is the size of a largest mutual-visibility set of $G$. Let $P$ be a set of $n\geq 3$ points in ${\mathbb R}^2$ in general position. The disjointness graph …

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://

This https://arxiv.org/abs/2403.03013 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The clique chromatic number of sparse random graphs
The clique chromatic number of a graph is the smallest number of colors in a vertex coloring so that no maximal clique is monochromatic. In this paper, we determine the order of magnitude of the clique chromatic number of the random graph G_{n,p} for most edge-probabilities p in the range n^{-2/5} \ll p \ll 1. This resolves open problems and questions of Lichev, Mitsche and Warnke as well as Alon and Krievelevich. One major proof difficulty stems from high-degree vertices, which prevent maxim…

Some Tur\'{a}n-type results for signless Laplacian spectral radius
Jian Zheng, Yongtao Li, Yi-Zheng Fan
https://arxiv.org/abs/2507.02263 https://

Some Turán-type results for signless Laplacian spectral radius
Half a century ago, Bollobás and Erdős [Bull. London Math. Soc. 5 (1973)] proved that every $n$-vertex graph $G$ with $e(G)\ge (1- \frac{1}{k} + \varepsilon )\frac{n^2}{2}$ edges contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\varepsilon}(\log n)$. A well-known theorem of Nikiforov [Combin. Probab. Comput. 18 (3) (2009)] asserts that if $G$ is an $n$-vertex graph with adjacency spectral radius $λ(G)\ge (1- \frac{1}{k} + \varepsilon)n$, then $G$ contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\var…

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…

A Fan-type condition involving bipartite independence number for hamiltonicity in graphs
Hongxi Liu, Long-Tu Yuan, Xiaowen Zhang
https://arxiv.org/abs/2506.02687

A Fan-type condition involving bipartite independence number for hamiltonicity in graphs
The bipartite independence number of a graph $G$, denoted by $\widetildeα(G)$, is defined as the smallest integer $q$ for which there exist positive integers $s$ and $t$ satisfying $s + t = q + 1$, such that for any two disjoint subsets $A, B \subseteq V(G)$ with $|A| = s$ and $|B| = t$, there exists an edge between $A$ and $B$. In this paper, we prove that for a $2$-connected graph $G$ of order at least three, if $\max\{d_G(x),d_G(y)\}\geq \widetildeα(G)$ for any pair of …

This https://arxiv.org/abs/2411.06177 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The number of trees in distance-hereditary graphs and their friends
Counting the number of spanning trees in specific classes of graphs has attracted increasing attention in recent years. In this note, we present unified proofs and generalizations of several results obtained in the 2020s. The main method is to study the behavior of the vertex (degree) enumerator of a distance-hereditary graph under the operations of copying vertices. Ehrenborg conjecture says that a Ferrer--Young graph maximizes the number of spanning trees among bipartite graphs with the sam…

The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture
Francesco Barioli, Shaun M. Fallat, Himanshu Gupta, Zhongshan Li
https://arxiv.org/abs/2505.24577

The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture
Since the transformative workshop by the American Institute of Mathematics on the minimum rank of a graph, two longstanding open problems have captivated the community interested in the minimum rank of graphs: the graph complement conjecture and the $δ$-conjecture. In this paper, we use a classical result of Mader (1972) to establish a weak version of the graph complement conjecture for all key minimum rank parameters. In addition, again using the same result of Mader, we present some extremal…

Embedding a Praeger-Xu graph into a surface
Zhaochen Ding, Zheng Guo, Luyi Liu
https://arxiv.org/abs/2507.01716 https://arxiv.org/pdf…

Embedding a Praeger-Xu graph into a surface
Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. This paper classifies all rotary maps whose underlying graphs are Praeger-Xu graphs, denoted $\operatorname{C}(p,r,s)$, for any odd prime $p$ that does not divide $r$. Our main result establishes a one-to-one correspondence between the isomorphism classes of these maps and the multiplicity-free representations of the dihedral group $\operatorname{D}_{2r}$ over the finite field $\mathbb{F}_p$. Thi…

This https://arxiv.org/abs/2412.16465 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Wheel-like bricks and minimal matching covered graphs
A connected graph G with at least two vertices is matching covered if each of its edges lies in a perfect matching. We say that an edge e in a matching covered graph G is removable if G-e is matching covered. A pair {e; f} of edges of a matching covered graph G is a removable doubleton if G-e-f is matching covered, but neither G-e nor G-f is. Removable edges and removable doubletons are called removable classes, introduced by Lovasz and Plummer in connection with ear decompositions of matching …

On the number of edges of restricted matchstick graphs
Panna Geh\'er, J\'anos Pach, Konrad Swanepoel, G\'eza T\'oth
https://arxiv.org/abs/2506.01589

On the number of edges of restricted matchstick graphs
A graph whose vertices are points in the plane and whose edges are noncrossing straight-line segments of unit length is called a \emph{matchstick graph}. We prove two somewhat counterintuitive results concerning the maximum number of edges of such graphs in two different scenarios. First, we show that there is a constant $c>0$ such that every triangle-free matchstick graph on $n$ vertices has at most $2n-c\sqrt{n}$ edges. This statement is not true for any $c>\sqrt2.$ We also prove that for…

Typical $T$-free graphs
Bruce Reed, Yelena Yuditsky
https://arxiv.org/abs/2506.01067 https://arxiv.org/pdf/2506.01067

Typical $T$-free graphs
We prove that for every tree $T$ which is not an edge, for almost every graph $G$ which does not contain $T$ as an induced subgraph, $V(G)$ has a partition into $α(T)-1$ parts certifying this fact. Each part induces a graph which is $P_4$-free and has further properties which depend on $T$. As a consequence we obtain good bounds (often tight up to a constant factor) on the number of $T$-free graphs and show in a follow-up paper~\cite{RY} that almost every $T$-free graph $G$ has chromatic numbe…

The asymptotic $\chi$-boundedness of hereditary families
Bruce Reed, Yelena Yuditsky
https://arxiv.org/abs/2506.01070 https://arxiv.o…

The asymptotic $χ$-boundedness of hereditary families
A family ${\cal F}$ of graphs is asymptotically $χ$-bounded with bounding function $f$ if almost every graph $G$ in the family satisfies $χ(G) \le f(ω(G))$. A graph is $H$-free if it does not contain $H$ as an induced subgraph. We ask which hereditary families are asymptotically $χ$-bounded, and discuss some related questions. We show that for every tree $T$, almost all $T$-free graphs $G$ satisfy $χ(G)=ω(G)$. We show that for every cycle $C_k$ except $C_6$, almost every $C_k$-free graph …