Tootfinder

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 433 nodes and 1941 edges.
Tags: Informational, Web gra…

Added a zoom level to the Category page on the Exocortex-Log app. Can make the graphs look a lot cleaner now.
Looking back over the last 100 months here, we can see in general my social life is quite seasonal -- Festivals are a lot of social all weekend long and a couple of them in a month really bumps up the hours from my usual habit of sitting alone in a dark room pressing buttons.
The peak in 2019 is a summer filled with Glasto and Noisily and another festival or camping trip I don’t seem to have recorded the name of.
Then clearly visible is the drop-off in social activity as the COVID pandemic hit. Virtual-Social (IE zoom meetings and the like) picked up quite a bit around there but had died back to almost nothing way before the hours spent with actual people started to tick up.
Annoyingly, I have my biggest gap in data right on top of the pandemic there, where I failed to back up for months and then data became corrupted.
When the data-hole is over we see social life still not really returning until the middle of 2021 and not really getting back into stride until summer 2022.
It remains much lower now on average with lower peaks than before the pandemic too. Multiple reasons.
Work is pretty constant all the way though other than the data-hole. Dipping when I take time off for social mostly.
That data-hole is annoying. Back up your data kids.
#lifeLog #app #exocortexLog

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 334 nodes and 32988 edges.
Tags: Informational, Web gr…

'graphviz' is a suite of programs for drawing graphs (In the nodes/edges senses, rather than upwards and to the right sense) - and it uses a file format called 'dot'. Lots of things generate dot output (such as systemd-analyze I mentioned) and it's really easy to generate from scripts and things. 'dotty' is probably the most common program in the suite.
There are some newer formats and programs - but this one is probably the most universal.

Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Marc Distel
https://arxiv.org/abs/2510.09063 https://arxiv.org/pdf/2510.09063

Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every $n$-vertex $K_h$-minor-free graph has treewidth $O_h(\sqrt{n})$. Recently, Distel, Dujmović, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [SIAM J. Discrete Math. 2024] refined this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $4$ graphs. We improve this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $3$ graphs.

Unifying Deductive and Abductive Reasoning in Knowledge Graphs with Masked Diffusion Model
Yisen Gao, Jiaxin Bai, Yi Huang, Xingcheng Fu, Qingyun Sun, Yangqiu Song
https://arxiv.org/abs/2510.11462

Unifying Deductive and Abductive Reasoning in Knowledge Graphs with Masked Diffusion Model
Deductive and abductive reasoning are two critical paradigms for analyzing knowledge graphs, enabling applications from financial query answering to scientific discovery. Deductive reasoning on knowledge graphs usually involves retrieving entities that satisfy a complex logical query, while abductive reasoning generates plausible logical hypotheses from observations. Despite their clear synergistic potential, where deduction can validate hypotheses and abduction can uncover deeper logical patte…

Efficient Learning-based Graph Simulation for Temporal Graphs
Sheng Xiang, Chenhao Xu, Dawei Cheng, Xiaoyang Wang, Ying Zhang
https://arxiv.org/abs/2510.05569 https://

Efficient Learning-based Graph Simulation for Temporal Graphs
Graph simulation has recently received a surge of attention in graph processing and analytics. In real-life applications, e.g. social science, biology, and chemistry, many graphs are composed of a series of evolving graphs (i.e., temporal graphs). While most of the existing graph generators focus on static graphs, the temporal information of the graphs is ignored. In this paper, we focus on simulating temporal graphs, which aim to reproduce the structural and temporal properties of the observed…

Sparse graphs and their Benjamini-Schramm limits: a spectral tour
Charles Bordenave
https://arxiv.org/abs/2510.10299 https://arxiv.org/pdf/2510.10299

Sparse graphs and their Benjamini-Schramm limits: a spectral tour
Sparse graphs with bounded average degree form a rich class of discrete structures where local geometry strongly influences global behavior. The Benjamini-Schramm (BS) convergence offers a natural framework to describe their asymptotic local structure. In this note, we survey spectral aspects of BS convergence and their applications, with a focus on random Schreier graphs and covering graphs. We review some recent progress on the spectral decomposition of the local operators on graphs. We discu…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 15 nodes and 50 edges.
Tags: Social, Fictional, Weighted

Integrating Structure-Aware Attention and Knowledge Graphs in Explainable Recommendation Systems
Shuangquan Lyu, Ming Wang, Huajun Zhang, Jiasen Zheng, Junjiang Lin, Xiaoxuan Sun
https://arxiv.org/abs/2510.10109

Integrating Structure-Aware Attention and Knowledge Graphs in Explainable Recommendation Systems
This paper designs and implements an explainable recommendation model that integrates knowledge graphs with structure-aware attention mechanisms. The model is built on graph neural networks and incorporates a multi-hop neighbor aggregation strategy. By integrating the structural information of knowledge graphs and dynamically assigning importance to different neighbors through an attention mechanism, the model enhances its ability to capture implicit preference relationships. In the proposed me…

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

R CHARTS | A collection of charts and graphs made with the R programming language
Over 1400 graphs with reproducible code divided in 8 big categories and over 50 chart types, in addition of tools to choose and create colors and color palettes

SVD-based ugmt-gft on directed product graphs
Guoyun Xie, Zhichao Zhang
https://arxiv.org/abs/2510.10532 https://arxiv.org/pdf/2510.10532

SVD-based ugmt-gft on directed product graphs
Traditional directed graph signal processing generally depends on fixed representation matrices, whose rigid structures limit the model's ability to adapt to complex graph topologies. To address this issue, this study employed the unified graph representation matrix (UGRM) to propose a generalized graph Fourier transform (UGRM-GFT) method based on singular value decomposition (SVD) for signal analysis on directed graphs and Cartesian product graphs. We defined UGRM-GFT for general directed grap…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 40 nodes and 100 edges.
Tags: Social, Fictional, Weighted

FOGMACHINE -- Leveraging Discrete-Event Simulation and Scene Graphs for Modeling Hierarchical, Interconnected Environments under Partial Observations from Mobile Agents
Lars Ohnemus, Nils Hantke, Max Wei{\ss}er, Kai Furmans
https://arxiv.org/abs/2510.09483

FOGMACHINE -- Leveraging Discrete-Event Simulation and Scene Graphs for Modeling Hierarchical, Interconnected Environments under Partial Observations from Mobile Agents
Dynamic Scene Graphs (DSGs) provide a structured representation of hierarchical, interconnected environments, but current approaches struggle to capture stochastic dynamics, partial observability, and multi-agent activity. These aspects are critical for embodied AI, where agents must act under uncertainty and delayed perception. We introduce FOGMACHINE , an open-source framework that fuses DSGs with discrete-event simulation to model object dynamics, agent observations, and interactions at scal…

On 16WW Data Collections and Graphs - Open for research #dataset - https://www.earth.org.uk/note-on-data.html

On 16WW Data Collections and Graphs
Open for research #dataset

On real functions with graphs either connected or locally connected
Gerald Kuba
https://arxiv.org/abs/2510.12450 https://arxiv.org/pdf/2510.12450

On real functions with graphs either connected or locally connected
Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the cardinality of G is c (the cardinality of the continuum) and the cardinality of H is 2^c, every space in the family G is completely metrizable, each element of H is a dense subset of the plane and the elements of the union of G and H are pairwise non-embeddable (i.p. pairwise non-homeomorphic) subspaces of the plane. O…

Boosted second moment method in random regular graphs
Bal\'azs Gerencs\'er, Viktor Harangi
https://arxiv.org/abs/2510.12600 https://arxiv.org/pdf/2…

Boosted second moment method in random regular graphs
Determining the asymptotic independence ratio of random regular graphs is a key challenge in the area of sparse random graphs. Due to the interpolation method, very good upper bounds are known, which are actually known to be sharp for sufficiently large degrees. This paper provides explicit lower bounds for given degrees $d$, beating the previous best bounds for $d \geq 10$. The starting point is a second moment argument that we can boost by arguing that the obtained independent set has a cer…

VisPile: A Visual Analytics System for Analyzing Multiple Text Documents With Large Language Models and Knowledge Graphs
Adam Coscia, Alex Endert
https://arxiv.org/abs/2510.09605

VisPile: A Visual Analytics System for Analyzing Multiple Text Documents With Large Language Models and Knowledge Graphs
Intelligence analysts perform sensemaking over collections of documents using various visual and analytic techniques to gain insights from large amounts of text. As data scales grow, our work explores how to leverage two AI technologies, large language models (LLMs) and knowledge graphs (KGs), in a visual text analysis tool, enhancing sensemaking and helping analysts keep pace. Collaborating with intelligence community experts, we developed a visual analytics system called VisPile. VisPile inte…

The chanciness of time
John M. Myers, Hadi Madjid
https://arxiv.org/abs/2511.08611 https://arxiv.org/pdf/2511.08611 https://arxiv.org/html/2511.08611
arXiv:2511.08611v1 Announce Type: new
Abstract: Digital network failures stemming from instabilities in measurements of temporal order motivate attention to concurrent events. A century of attempts to resolve the instabilities have never eliminated them. Do concurrent events occur at indeterminate times, or are they better seen as events to which the very concept of temporal order cannot apply? Logical dependencies of messages propagating through digital networks can be represented by marked graphs on which tokens are moved in formal token games. However, available mathematical formulations of these token games invoke "markings"-- global snapshots of the locations of tokens on the graph. The formulation in terms of global snapshots is misleading, because distributed networks are never still: they exhibit concurrent events inexpressible by global snapshots. We reformulate token games used to represent digital networks so as to express concurrency. The trick is to replace global snapshots with "local snapshots." Detached from any central clock, a local snapshot records an action at a node during a play of a token game. Assemblages of local records define acyclic directed graphs that we call history graphs. We show how history graphs represent plays of token games with concurrent motions, and, importantly, how history graphs can represent the history of a network operating while undergoing unpredictable changes.
toXiv_bot_toot

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Zhiqiang Yuan, Wenjun Mao, Zhuo Chen, Xiyue Shang, Chong Wang, Yiling Lou, Xin Peng
https://arxiv.org/abs/2510.10956

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Translating C code into safe Rust is an effective way to ensure its memory safety. Compared to rule-based translation which produces Rust code that remains largely unsafe, LLM-based methods can generate more idiomatic and safer Rust code because LLMs have been trained on vast amount of human-written idiomatic code. Although promising, existing LLM-based methods still struggle with project-level C-to-Rust translation. They typically partition a C project into smaller units (\eg{} functions) base…

Loop functions of sunset graphs in 2 1 space-time dimensions
N. Kaiser
https://arxiv.org/abs/2510.08704 https://arxiv.org/pdf/2510.08704

Loop functions of sunset graphs in 2+1 space-time dimensions
In these notes the relativistic $n$-body phase-phase is calculated iteratively in $2+1$ space-time dimensions for all $n$. The obtained result shows a simple power-law behavior $α_n (μ-M)^{n-2}/μ$ with a dependence only on the total mass $M=m_1+\dots + m_n$. As a consequence of this feature, the $(n-1)$-loop integrals $J_n(-q^2)$ associated to sunset graphs with $n$ internal lines can be expressed through of elementary (arctangent and logarithmic) functions, modulo polynomial terms in $q^2$ …

Optimizing Administrative Divisions: A Vertex $k$-Center Approach for Edge-Weighted Road Graphs
Peteris Daugulis
https://arxiv.org/abs/2510.09334 https://a…

Optimizing Administrative Divisions: A Vertex $k$-Center Approach for Edge-Weighted Road Graphs
Efficient and equitable access to municipal services hinges on well-designed administrative divisions. It requires ongoing adaptation to changing demographics, infrastructure, and economic factors. This article proposes a novel transparent data-driven method for territorial division based on the Voronoi partition of edge-weighted road graphs and the vertex $k$-center problem as a special case of the minimax facility location problem. By considering road network structure and strategic placement…

The Homology Groups of Zero Divisor Graphs of Finite Commutative Rings
Fenglin Li
https://arxiv.org/abs/2510.14224 https://arxiv.org/pdf/2510.14224

When I am King, all graphs will be required to use the label "lots" along the Y-axis.
https://mastodon.gamedev.place/@eniko/115373539503634831

Eniko Fox (@eniko@mastodon.gamedev.place)
Attached: 1 image people will be like "i've got the summer flu" and this is the wastewater graph for their area

KeySG: Hierarchical Keyframe-Based 3D Scene Graphs
Abdelrhman Werby, Dennis Rotondi, Fabio Scaparro, Kai O. Arras
https://arxiv.org/abs/2510.01049 https://…

KeySG: Hierarchical Keyframe-Based 3D Scene Graphs
In recent years, 3D scene graphs have emerged as a powerful world representation, offering both geometric accuracy and semantic richness. Combining 3D scene graphs with large language models enables robots to reason, plan, and navigate in complex human-centered environments. However, current approaches for constructing 3D scene graphs are semantically limited to a predefined set of relationships, and their serialization in large environments can easily exceed an LLM's context window. We introdu…

Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
Qi Yan, Xiang-Dong Li
https://arxiv.org/abs/2510.09383 https://ar…

Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
We are concerned with a stochastic mean curvature flow of graphs with extra force over a periodic domain of any dimension. Based on compact embedding method of variational SPDE, we prove the existence of martingale solution. Moreover, we derive the small perturbation limit of the stochastic weighted mean curvature flow.

The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs
Zylan Benjert, Kostas Lakis, Johannes Lengler, Raghu Raman Ravi
https://arxiv.org/abs/2510.12543 https://

The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs
We prove that the diameter of threshold (zero temperature) Geometric Inhomogeneous Random Graphs (GIRG) is $Θ(\log n)$. This has strong implications for the runtime of many distributed protocols on those graphs, which often have runtimes bounded as a function of the diameter. The GIRG model exhibits many properties empirically found in real-world networks, and the runtime of various practical algorithms has empirically been found to scale in the same way for GIRG and for real-world networks,…

Plotted my MacBook Pro's battery usage history based on almost 4 years of coconutBattery data for shits and giggles

caida_as: CAIDA AS graphs (2004-2007)
A sequence of 122 network snapshots denoting Autonomous System (AS) relationships on the Internet, from 2004-2007, inferred using the Serial-1 method from RouteViews BGP table snapshots and a set of heuristics.
This network has 24454 nodes and 99660 edges.
Tags: Technological, Communication, Unweighted, Temporal

Root Cause Analysis of Outliers in Unknown Cyclic Graphs
Daniela Schkoda, Dominik Janzing
https://arxiv.org/abs/2510.06995 https://arxiv.org/pdf/2510.06995…

Root Cause Analysis of Outliers in Unknown Cyclic Graphs
We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our m…

Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$
Fabien de Montgolfier (IRIF), Renaud Torfs (IRIF)
https://arxiv.org/abs/2510.04621

Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$
There are three usual definitions of a maximum bipartite clique (biclique) in a bipartite graph\,: either maximizing the number of vertices, or of edges, or finding a maximum balanced biclique. The first problem can be solved in polynomial time, the last ones are NP-complete. Here we show how these three problems may be efficiently solved for two classes of bipartite graphs: Star123-free twin-free graphs, and bounded bimodularwidth twin-free graphs, a class that may be defined using bimodular d…

Structure-Aware Spectral Sparsification via Uniform Edge Sampling
Kaiwen He, Petros Drineas, Rajiv Khanna
https://arxiv.org/abs/2510.12669 https://arxiv.or…

Structure-Aware Spectral Sparsification via Uniform Edge Sampling
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges proportionally to their effective resistances, but require expensive preprocessing to estimate these resistances. We study whether uniform edge sampling-a simple, structure-agnostic strategy-can suffice for spectral clustering. Our main result shows that for graphs adm…

From Knowledge to Treatment: Large Language Model Assisted Biomedical Concept Representation for Drug Repurposing
Chengrui Xiang, Tengfei Ma, Xiangzheng Fu, Yiping Liu, Bosheng Song, Xiangxiang Zeng
https://arxiv.org/abs/2510.12181

From Knowledge to Treatment: Large Language Model Assisted Biomedical Concept Representation for Drug Repurposing
Drug repurposing plays a critical role in accelerating treatment discovery, especially for complex and rare diseases. Biomedical knowledge graphs (KGs), which encode rich clinical associations, have been widely adopted to support this task. However, existing methods largely overlook common-sense biomedical concept knowledge in real-world labs, such as mechanistic priors indicating that certain drugs are fundamentally incompatible with specific treatments. To address this gap, we propose LLaDR, …

2-Factors in Graphs
Jan van den Heuvel, Bjarne Toft
https://arxiv.org/abs/2510.11486 https://arxiv.org/pdf/2510.11486…

2-Factors in Graphs
An account of 2-factors in graphs and their history is presented. We give a direct graph-theoretic proof of the 2-Factor Theorem and a new variant of it, and also a new complete characterisation of the maximal graphs without 2-factors. This is based on the important works of Tibor Gallai on 1-factors and of Hans-Boris Belck on k-factors, both published in 1950 and independently containing the theory of alternating chains. We also present an easy proof that a $(2k+1)$-regular graph with at most …

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- First Order Logic and Twin-Width in Tournaments and Dense Oriented Graphs
Colin Geniet, St\'ephan Thomass\'e

Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
Daniil Kochergin
https://arxiv.org/abs/2510.10255 https://ar…

Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
We studied single-particle Anderson localization in ensembles of graphs that correspond to chiral and Bogoliubov-de Gennes (BdG) symmetry classes. For a random biregular bipartite graph with chiral symmetry, the density of states was found using the cavity approach. Calculating the fractal dimension shows the effects of disordered zero modes. For Bogoliubov-de Gennes ensembles with an underlying random regular graph (RRG), the density of states was calculated both numerically and analytically. …

On the Expressiveness of Languages for Querying Property Graphs in Relational Databases
Hadar Rotschield, Liat Peterfreund
https://arxiv.org/abs/2510.07062 https://

On the Expressiveness of Languages for Querying Property Graphs in Relational Databases
SQL/PGQ is the emerging ISO standard for querying property graphs defined as views over relational data. We formalize its expressive power across three fragments: the read-only core, the read-write extension, and an extended variant with richer view definitions. Our results show that graph creation plays a central role in determining the expressiveness. The read-only fragment is strictly weaker than the read-write fragment, and the latter is still below the complexity class NL. Extending view d…

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 8361 nodes and 15751 edges.
Tags: Social, Collaboration…

Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
Minsung Kho, Norton Lee, Rak-Kyeong Seong
https://arxiv.org/abs/2510.12290 https://

Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d N=1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds. We present a complete classification of dimer integrable systems corresponding to the 30 brane tilings whose toric Calabi-Yau 3-folds are given by the 16 reflexive polygons in 2 dimensions. For each dimer integrable system associated to a reflexive polygon, we present the Casimirs, the single Hamiltonian built from 1-loops, the …

Form uniqueness for graphs with weakly spherically symmetric ends
Luis Hernandez, Sean Ku, Jun Masamune, Genevieve Romanelli, Rados{\l}aw K. Wojciechowski
https://arxiv.org/abs/2509.22967

Form uniqueness for graphs with weakly spherically symmetric ends
We give characterizations for the failure of form uniqueness on weakly spherically symmetric graphs. The first characterization is in terms of the graph structure, the second involves the capacity of a Cauchy boundary. We also discuss the stability of form uniqueness and give characterizations for graphs which, following the removal of a set, consist of a disjoint union of weakly spherically symmetric graphs.

GraphMERT: Efficient and Scalable Distillation of Reliable Knowledge Graphs from Unstructured Data
Margarita Belova, Jiaxin Xiao, Shikhar Tuli, Niraj K. Jha
https://arxiv.org/abs/2510.09580

GraphMERT: Efficient and Scalable Distillation of Reliable Knowledge Graphs from Unstructured Data
Researchers have pursued neurosymbolic artificial intelligence (AI) applications for nearly three decades because symbolic components provide abstraction while neural components provide generalization. Thus, a marriage of the two components can lead to rapid advancements in AI. Yet, the field has not realized this promise since most neurosymbolic AI frameworks fail to scale. In addition, the implicit representations and approximate reasoning of neural approaches limit interpretability and trust…

Reasoning by Exploration: A Unified Approach to Retrieval and Generation over Graphs
Haoyu Han, Kai Guo, Harry Shomer, Yu Wang, Yucheng Chu, Hang Li, Li Ma, Jiliang Tang
https://arxiv.org/abs/2510.07484

Reasoning by Exploration: A Unified Approach to Retrieval and Generation over Graphs
Reasoning over structured graphs remains a fundamental challenge for Large Language Models (LLMs), particularly when scaling to large graphs. Existing approaches typically follow the retrieval-augmented generation (RAG) paradigm: first retrieving subgraphs relevant to the query and then generating answers conditioned on the retrieved subgraphs. However, such two-phase pipelines often struggle to faithfully incorporate graph structure, since the generation process is ultimately constrained by th…

Metric Dimension of Generalized Theta Graphs
Nadia Benakli, Nicole Froitzheim, David Martinez
https://arxiv.org/abs/2510.12100 https://arxiv.org/pdf/2510.1…

Metric Dimension of Generalized Theta Graphs
A vertex $w$ in a graph $G$ is said to resolve two vertices $u$ and $v$ if $d(w,u)\neq d(w, v)$. A set $W$ of vertices is a resolving set for $G$ if every pair of distinct vertices is resolved by some vertex in $W$. The metric dimension of $G$ is the minimum cardinality of such a set. In this paper, we investigate the metric dimension of generalized theta graphs, providing exact values and structural insights for several subclasses.

Planted clique recovery in random geometric graphs
Konstantin Avrachenkov, Andrei Bobu, Nelly Litvak, Riccardo Michielan
https://arxiv.org/abs/2510.12365 https://

Planted clique recovery in random geometric graphs
We investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance of these methods under varying regimes of key parameters, namely the average degree of the graph and the size of the planted clique. We demonstrate that exact recovery is achieved with high probability as the graph size increases, in a specific set of parame…

On 16WW Data Collections and Graphs - Open for research #dataset - https://www.earth.org.uk/note-on-data.html

On 16WW Data Collections and Graphs
Open for research #dataset

Two-Dimensional Graph Bi-Fractional Fourier Transform
Mingzhi Wang, Zhichao Zhang
https://arxiv.org/abs/2510.11279 https://arxiv.org/pdf/2510.11279

Two-Dimensional Graph Bi-Fractional Fourier Transform
Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its adaptability to heterogeneous signals. We proposed the two-dimensional graph bi-fractional Fourier transform (2D-GBFRFT), which assigns independent fractional orders to the factor graphs of a Cartesian product while preserving separability. We established inver…

ReeMark: Reeb Graphs for Simulating Patterns of Life in Spatiotemporal Trajectories
Anantajit Subrahmanya, Chandrakanth Gudavalli, Connor Levenson, Umang Garg, B. S. Manjunath
https://arxiv.org/abs/2510.03152

ReeMark: Reeb Graphs for Simulating Patterns of Life in Spatiotemporal Trajectories
Accurately modeling human mobility is critical for urban planning, epidemiology, and traffic management. In this work, we introduce Markovian Reeb Graphs, a novel framework for simulating spatiotemporal trajectories that preserve Patterns of Life (PoLs) learned from baseline data. By combining individual- and population-level mobility structures within a probabilistic topological model, our approach generates realistic future trajectories that capture both consistency and variability in daily l…

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 8361 nodes and 15751 edges.
Tags: Social, Collaboration…

Parameterized Complexity of Temporal Connected Components: Treewidth and k-Path Graphs
Argyrios Deligkas, Michelle D\"oring, Eduard Eiben, Tiger-Lily Goldsmith, George Skretas, Georg Tennigkeit
https://arxiv.org/abs/2510.05806

Parameterized Complexity of Temporal Connected Components: Treewidth and k-Path Graphs
We study the parameterized complexity of maximum temporal connected components (tccs) in temporal graphs, i.e., graphs that deterministically change over time. In a tcc, any pair of vertices must be able to reach each other via a time-respecting path. We consider both problems of maximum open tccs (openTCC), which allow temporal paths through vertices outside the component, and closed tccs (closedTCC) which require at least one temporal path entirely within the component for every pair. We focu…

A class of graphs: Bridging structures in commutative algebra
Fahimeh Khosh-Ahang Ghasr
https://arxiv.org/abs/2510.06729 https://arxiv.org/pdf/2510.06729…

A class of graphs: Bridging structures in commutative algebra
We characterize classes of simplicial complexes $Δ$ for which the generators of the determinantal facet ideal $J_Δ$ form a reduced Gröbner basis. This result provides a new proof for a known fact about determinantal ideals in a special case and extends several existing results concerning binomial edge ideals and determinantal facet ideals. We also introduce and examine generalizations of interval graphs and proper interval graphs, aiming to establish equivalent characterizations for these …

Minima and Critical Points of the Bethe Free Energy Are Invariant Under Deformation Retractions of Factor Graphs
Gr\'egoire Sergeant-Perthuis, L\'eo Boitel
https://arxiv.org/abs/2510.05380

Minima and Critical Points of the Bethe Free Energy Are Invariant Under Deformation Retractions of Factor Graphs
In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a partially ordered set (poset). Inference on such probabilistic models cannot be performed exactly due to cycles in the underlying structures of interaction. Instead, one resorts to approximate variational inference by optimizing the Bethe free energy. Critical points of the Bethe free energy correspond to fixed point…

Super-minimally $3$-connected graphs
Wayne Ge
https://arxiv.org/abs/2510.06392 https://arxiv.org/pdf/2510.06392

Super-minimally $3$-connected graphs
In this paper, we introduce super-minimally $k$-connected graphs, those $k$-connected graphs in which no proper subgraph is $k$-connected. For $k$ greater than or equal to three, this class lies strictly between the classes of minimally $k$-connected graphs and uniformly $k$-connected graphs. In particular, we determine the minimum number of degree-$3$ vertices in a super-minimally $3$-connected graph, thereby extending a result of Halin on minimally $3$-connected graphs. In addition, we determ…

What Do Temporal Graph Learning Models Learn?
Abigail J. Hayes, Tobias Schumacher, Markus Strohmaier
https://arxiv.org/abs/2510.09416 https://arxiv.org/pdf…

What Do Temporal Graph Learning Models Learn?
Learning on temporal graphs has become a central topic in graph representation learning, with numerous benchmarks indicating the strong performance of state-of-the-art models. However, recent work has raised concerns about the reliability of benchmark results, noting issues with commonly used evaluation protocols and the surprising competitiveness of simple heuristics. This contrast raises the question of which properties of the underlying graphs temporal graph learning models actually use to f…

MultiCNKG: Integrating Cognitive Neuroscience, Gene, and Disease Knowledge Graphs Using Large Language Models
Ali Sarabadani, Kheirolah Rahsepar Fard
https://arxiv.org/abs/2510.06742

MultiCNKG: Integrating Cognitive Neuroscience, Gene, and Disease Knowledge Graphs Using Large Language Models
The advent of large language models (LLMs) has revolutionized the integration of knowledge graphs (KGs) in biomedical and cognitive sciences, overcoming limitations in traditional machine learning methods for capturing intricate semantic links among genes, diseases, and cognitive processes. We introduce MultiCNKG, an innovative framework that merges three key knowledge sources: the Cognitive Neuroscience Knowledge Graph (CNKG) with 2.9K nodes and 4.3K edges across 9 node types and 20 edge types…

On positive solutions of Lane-Emden equations on the integer lattice graphs
Huyuan Chen, Bobo Hua, Feng Zhou
https://arxiv.org/abs/2510.08947 https://arxiv…

On positive solutions of Lane-Emden equations on the integer lattice graphs
In this paper, we investigate the existence and nonexistence of positive solutions to the Lane-Emden equations $$ -Δu = Q |u|^{p-2}u $$ on the $d$-dimensional integer lattice graph $\mathbb{Z}^d$, as well as in the half-space and quadrant domains, under the zero Dirichlet boundary condition in the latter two cases. Here, $d \geq 2$, $p > 0$, and $Q$ denotes a Hardy-type positive potential satisfying $Q(x) \sim (1+|x|)^{-α}$ with $α\in [0, +\infty]$. \smallskip We identi…

Construction of infinitely many trace-minimal graphs with maximum number of spanning trees
Pablo Romero, Louis Petingi
https://arxiv.org/abs/2510.02548 https://

Construction of infinitely many trace-minimal graphs with maximum number of spanning trees
A longstanding problem in spectral graph theory asks for graphs with maximum number of spanning trees among all connected simple graphs with a prescribed number of vertices and edges. Such graphs are called t-optimal graphs. Petingi and Rodríguez [Discrete Math. 244 (2002), 351--373] achieved in finding infinitely many t-optimal graphs. Basically, they reduced the problem of finding t-optimal graphs to the determination of almost-regular graphs with minimum number of induced 3-paths. In this…

route_views: Route Views AS graphs (1997-1998)
733 daily network snapshots denoting BGP traffic among autonomous systems (ASs) on the Internet, from the Oregon Route Views Project, spanning 8 November 1997 to 2 January 2000. Data collected by NLANR/MOAT.
This network has 3271 nodes and 6246 edges.
Tags: Technological, Communication, Unweighted, Temporal

On 16WW Data Collections and Graphs - Open for research #dataset - https://www.earth.org.uk/note-on-data.html

On 16WW Data Collections and Graphs
Open for research #dataset

Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set
Anton Herrmann, Christian Komusiewicz, Nils Morawietz, Frank Sommer
https://arxiv.org/abs/2510.08124 https:…

Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set
A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is \textsc{Timeline Vertex Cover} (also known as \textsc{MinTimeline$_\infty$}), a temporal analogue to the classical \textsc{Vertex Cover} problem. In this problem, one is given a temporal graph $\mathcal{G}$ and two integers $k$ and $\ell$, and the goal is to cover each edge of each snapsho…

Rare event probabilities in Random Geometric Graphs
Prabhanka Deka, Fangzhou Luo, Baichuan Wu
https://arxiv.org/abs/2510.09196 https://arxiv.org/pdf/2510.0…

Rare event probabilities in Random Geometric Graphs
In this paper, we study rare events in spherical and Gaussian random geometric graphs in high dimensions. In these models, the vertices correspond to points sampled uniformly at random on the $d$ dimensional unit sphere or correspond to $d$ dimensional standard Gaussian vectors, and edges are added between two vertices if the inner-product between their corresponding points are greater than a threshold $t_p$, chosen such that the probability of having an edge is equal to $p$. We focus on two pr…

Conformalized Gaussian processes for online uncertainty quantification over graphs
Jinwen Xu, Qin Lu, Georgios B. Giannakis
https://arxiv.org/abs/2510.06181 https://

Conformalized Gaussian processes for online uncertainty quantification over graphs
Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by devising topology-aware kernel functions. However, such GP-based approaches are limited not only by the prohibitive computational complexity, but also the strict modeling assumptions that might yield poor coverage, especially with labels arriving on the fly. To…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 20 nodes and 30 edges.
Tags: Social, Fictional, Weighted

Nowhere-zero flows on signed supereulerian graphs
Chao Wen, Qiang Sun, Chao Zhang
https://arxiv.org/abs/2510.08192 https://arxiv.org/pdf/2510.08192

Nowhere-zero flows on signed supereulerian graphs
In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero 6-flow. We verify this conjecture for the class of flow-admissible signed graphs possessing a spanning even Eulerian subgraph, which includes as a special case all signed graphs with a balanced Hamiltonian circuit. Furthermore, we show that this result is sharp by citing a known infinite family of signed graphs with a balanced Hamiltonian circuit that do not admit a nowhere-zero 5-flow. Our proof relies o…

On Stable Cutsets in General and Minimum Degree Constrained Graphs
Mats Vroon, Hans L. Bodlaender
https://arxiv.org/abs/2510.09432 https://arxiv.org/pdf/25…

On Stable Cutsets in General and Minimum Degree Constrained Graphs
A stable cutset is a set of vertices $S$ of a connected graph, that is pairwise non-adjacent and when deleting $S$, the graph becomes disconnected. Determining the existence of a stable cutset in a graph is known to be NP-complete. In this paper, we introduce a new exact algorithm for Stable Cutset. By branching on graph configurations and using the $O^*(1.3645)$ algorithm for the (3,2)-Constraint Satisfaction Problem presented by Beigel and Eppstein, we achieve an improved running time of $O^*…

Dominating Hadwiger's Conjecture for graphs $G$ with $\alpha(G)=2$
Michael Scully, Zi-Xia Song
https://arxiv.org/abs/2510.12564 https://arxiv.org/pdf/2…

Dominating Hadwiger's Conjecture for graphs $G$ with $α(G)=2$
Hadwiger's Conjecture from 1943 states that every graph with chromatic number $t$ contains a $K_t$ minor. Illingworth and Wood [arXiv:2405.14299] introduced the concept of a ``dominating $K_t$ minor'' and asked whether every graph with chromatic number $t$ contains a dominating $K_t$ minor. This question is a substantial strengthening of Hadwiger's Conjecture. Norin referred to it as the ``Dominating Hadwiger's Conjecture'' and believes it is likely false. In this paper we first observe that a …

FusionAdapter for Few-Shot Relation Learning in Multimodal Knowledge Graphs
Ran Liu, Yuan Fang, Xiaoli Li
https://arxiv.org/abs/2510.00894 https://arxiv.or…

FusionAdapter for Few-Shot Relation Learning in Multimodal Knowledge Graphs
Multimodal Knowledge Graphs (MMKGs) incorporate various modalities, including text and images, to enhance entity and relation representations. Notably, different modalities for the same entity often present complementary and diverse information. However, existing MMKG methods primarily align modalities into a shared space, which tends to overlook the distinct contributions of specific modalities, limiting their performance particularly in low-resource settings. To address this challenge, we pro…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 28 nodes and 75 edges.
Tags: Social, Fictional, Weighted

On the Fourier dimension of fractional Brownian graphs
Cheuk Yin Lee, Samy Tindel
https://arxiv.org/abs/2510.09818 https://arxiv.org/pdf/2510.09818

On the Fourier dimension of fractional Brownian graphs
In this note we prove that the Fourier dimension of the graph $G(B)$ of a fractional Brownian motion $B$ with Hurst parameter $H\in(0,1/2)$ is equal to 1. This finishes to solve a conjecture by Fraser and Sahlsten. It also yields an exact formula for the gap $\dim_{\rm H}(G(B)) - \dim_{\rm F}(G(B))$ between the Hausdorff dimension and the Fourier dimension of $G(B)$. The proof is based on an intricate combinatorics procedure for multiple integrals related to the covariance function of the fract…

Dominating Hadwiger's Conjecture holds for all $2K_2$-free graphs
Zi-Xia Song, Thomas Tibbetts
https://arxiv.org/abs/2510.12567 https://arxiv.org/pdf/2…

Dominating Hadwiger's Conjecture holds for all $2K_2$-free graphs
A dominating $K_t$ minor in a graph $G$ is a sequence $(T_1,\dots,T_t)$ of pairwise disjoint non-empty connected subgraphs of $G$, such that for $1 \leq i

Revisiting Node Affinity Prediction in Temporal Graphs
Krishna Sri Ipsit Mantri, Or Feldman, Moshe Eliasof, Chaim Baskin
https://arxiv.org/abs/2510.06940 https://

Revisiting Node Affinity Prediction in Temporal Graphs
Node affinity prediction is a common task that is widely used in temporal graph learning with applications in social and financial networks, recommender systems, and more. Recent works have addressed this task by adapting state-of-the-art dynamic link property prediction models to node affinity prediction. However, simple heuristics, such as Persistent Forecast or Moving Average, outperform these models. In this work, we analyze the challenges in training current Temporal Graph Neural Networks …

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 433 nodes and 1941 edges.
Tags: Informational, Web gra…

A note on the number of non-cycle components in a pseudo 2-factor of graphs
Masaki Kashima
https://arxiv.org/abs/2510.12155 https://arxiv.org/pdf/2510.1215…

A note on the number of non-cycle components in a pseudo 2-factor of graphs
A pseudo 2-factor of a graph is a spanning subgraph such that each component is $K_1$, $K_2$, or a cycle. This notion was introduced by Bekkai and Kouider in 2009, where they showed that every graph $G$ has a pseudo 2-factor with at most $α(G)-δ(G)+1$ components that are not cycles. For a graph $G$ and a set of vertices $S$, let $δ_G(S)$ denote the minimum degree of vertices in $S$. In this note, we show that every graph $G$ has a pseudo 2-factor with at most $f(G)$ components that are not c…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 27 nodes and 96 edges.
Tags: Social, Fictional, Weighted

Improved bounds for the minimum degree of minimal multicolor Ramsey graphs
Yamaan Attwa, Sam Mattheus, Tibor Szab\'o, Jacques Verstraete
https://arxiv.org/abs/2510.09068 htt…

Improved bounds for the minimum degree of minimal multicolor Ramsey graphs
We provide two novel constructions of $r$ edge-disjoint $K_{k+1}$-free graphs on the same vertex set, each of which has the property that every small induced subgraph contains a complete graph on $k$ vertices. The main novelty of our argument is the combination of an algebraic and a probabilistic coloring scheme, which utilizes the beneficial algebraic and combinatorial properties of the Hermitian unital. These constructions improve on a number of upper bounds on the smallest possible minimum d…

Ontolearn-A Framework for Large-scale OWL Class Expression Learning in Python
Caglar Demir, Alkid Baci, N'Dah Jean Kouagou, Leonie Nora Sieger, Stefan Heindorf, Simon Bin, Lukas Bl\"ubaum, Alexander Bigerl, Axel-Cyrille Ngonga Ngomo
https://arxiv.org/abs/2510.11561

Ontolearn-A Framework for Large-scale OWL Class Expression Learning in Python
In this paper, we present Ontolearn-a framework for learning OWL class expressions over large knowledge graphs. Ontolearn contains efficient implementations of recent stateof-the-art symbolic and neuro-symbolic class expression learners including EvoLearner and DRILL. A learned OWL class expression can be used to classify instances in the knowledge graph. Furthermore, Ontolearn integrates a verbalization module based on an LLM to translate complex OWL class expressions into natural language sen…

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 346 nodes and 26832 edges.
Tags: Informational, Web gr…

Isolation of non-triangle cycles in graphs
Peter Borg, Dayle Scicluna
https://arxiv.org/abs/2510.08361 https://arxiv.org/pdf/2510.08361

Isolation of non-triangle cycles in graphs
Given a set $\mathcal{F}$ of graphs, we call a copy of a graph in $\mathcal{F}$ an $\mathcal{F}$-graph. The $\mathcal{F}$-isolation number of a graph $G$, denoted by $ι(G, \mathcal{F})$, is the size of a smallest set $D$ of vertices of $G$ such that the closed neighbourhood of $D$ intersects the vertex sets of the $\mathcal{F}$-graphs contained by $G$ (equivalently, $G-N[D]$ contains no $\mathcal{F}$-graph). Let $\mathcal{C}$ be the set of cycles, and let $\mathcal{C}'$ be the set of non-trian…

Inductive inference of gradient-boosted decision trees on graphs for insurance fraud detection
F\'elix Vandervorst, Bruno Deprez, Wouter Verbeke, Tim Verdonck
https://arxiv.org/abs/2510.05676

Inductive inference of gradient-boosted decision trees on graphs for insurance fraud detection
Graph-based methods are becoming increasingly popular in machine learning due to their ability to model complex data and relations. Insurance fraud is a prime use case, since false claims are often the result of organised criminals that stage accidents or the same persons filing erroneous claims on multiple policies. One challenge is that graph-based approaches struggle to find meaningful representations of the data because of the high class imbalance present in fraud data. Another is that insu…

Putting Tutte's counterexample to Tait's conjecture in perspective to hamiltonicity and non-hamiltonicity in certain planar cubic graphs
Herbert Fleischner, Enrico Iurlano, G\"unther R. Raidl
https://arxiv.org/abs/2510.08310

Putting Tutte's counterexample to Tait's conjecture in perspective to hamiltonicity and non-hamiltonicity in certain planar cubic graphs
Using the graphs of prisms and Tutte Fragments, we construct an infinite family of hamiltonian and non-hamiltonian graphs in which Tutte's counterexample to Tait's conjecture appears in a certain sense as a minimal element. We observe that generalizations of the minimum-cardinality counterexamples of Holton and McKay to Tait's conjecture are as well contained in this family.

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 300 nodes and 1155 edges.
Tags: Informational, Web gra…

Extending Thomassen's conjecture to directed graphs
Micha Christoph, Barnab\'as Janzer, Kalina Petrova, Raphael Steiner
https://arxiv.org/abs/2510.11311 https://

Extending Thomassen's conjecture to directed graphs
A famous conjecture by Thomassen from 1983 asserts that for any given $k,g\in \mathbb{N}$ there exists some $d=d(k,g)\in \mathbb{N}$ such that every graph of minimum degree at least $d$ contains a subgraph of minimum degree at least $k$ and girth at least $g$. In this paper, we initiate the systematic study of the directed analogs of Thomassen's conjecture one obtains when replacing minimum degree by minimum out-degree. Concretely, we study which digraphs $F$ are avoidable in the sense that the…

New lower bounds on the non-repetitive chromatic number of some graphs
Tianyi Tao, Junchi Zhang, Wentao Zhang, Alex Toole
https://arxiv.org/abs/2510.11263 https://

New lower bounds on the non-repetitive chromatic number of some graphs
A graph \( G \) is said to be (vertex) non-repetitively colored if no simple path in \( G \) has a sequence of vertex colors that forms a repetition. Formally, a coloring \( c: V(G) \to \{1, 2, \dots, k\} \) is non-repetitive if, for every path \(\langle v_1, v_2, \dots, v_{2m} \rangle\) in \( G \), the sequence of colors \( c(v_1), c(v_2), \dots, c(v_{2m}) \) is not of the form \( ww \), where \( w \) is a sequence of \( m \) colors. The minimum number of colors required for such a coloring is…

Extending Ghouila-Houri's Characterization of Comparability Graphs to Temporal Graphs
Pierre Charbit, Michel Habib, Amalia Sorondo
https://arxiv.org/abs/2510.06849 https://

Extending Ghouila-Houri's Characterization of Comparability Graphs to Temporal Graphs
An orientation of a given static graph is called transitive if for any three vertices $a,b,c$, the presence of arcs $(a,b)$ and $(b,c)$ forces the presence of the arc $(a,c)$. If only the presence of an arc between $a$ and $c$ is required, but its orientation is unconstrained, the orientation is called quasi-transitive. A fundamental result presented by Ghouila-Houri guarantees that any static graph admitting a quasi-transitive orientation also admits a transitive orientation. In a seminal work…

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 433 nodes and 1941 edges.
Tags: Informational, Web gra…

Advances in the Shannon Capacity of Graphs
Nitay Lavi, Igal Sason
https://arxiv.org/abs/2509.24600 https://arxiv.org/pdf/2509.24600

Advances in the Shannon Capacity of Graphs
This paper studies several research directions concerning the Shannon capacity of graphs. Building on Schrijver's recent framework, we establish sufficient conditions under which the Shannon capacity of a polynomial in graphs equals the corresponding polynomial of the individual capacities, thereby simplifying their evaluation. We derive exact values and new bounds for the Shannon capacity of two families of graphs: the q-Kneser graphs and the Tadpole graphs. Furthermore, we construct graphs wh…

webkb: WebKB graphs (1998)
Web graphs crawled from four Computer Science departments in 1998, with each page manually classified into one of 7 categories: course, department, faculty, project, staff, student, or other. All graphs included in a single .zip; also included are 'co-citation' graphs, which links i and j if they both point to some k. Edge weights count the number of links from i to j.
This network has 334 nodes and 32988 edges.
Tags: Informational, Web gr…

Characterizing Graphs as Algebraic Squares
Karen L. Collins, David Galvin, Christine A. Kelley, Emily McMillon, Amanda Redlich
https://arxiv.org/abs/2510.05372 https://

Characterizing Graphs as Algebraic Squares
Graphs that are squares under the gluing algebra arise in the study of homomorphism density inequalities such as Sidorenko's conjecture. Recent work has focused on these homomorphism density applications. This paper takes a new perspective and focuses on the graph properties of arbitrary square graphs, not only those relevant to homomorphism conjectures and theorems. We develop a set of necessary and/or sufficient conditions for a graph to be square. We apply these conditions to categorize se…

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 67 nodes and 186 edges.
Tags: Social, Fictional, Weighted

Closing paths to cycles in symmetric graphs
Martin Milani\v{c}, {\DJ}or{\dj}e Mitrovi\'c
https://arxiv.org/abs/2510.05404 https://arxiv.org/pdf/2510.05…

Closing paths to cycles in symmetric graphs
It was shown by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2022 that every induced $2$-edge path in a vertex-transitive graph closes to an induced cycle. Similar results were obtained for 3-edge paths closing to cycles in edge-transitive graphs, where the cycle can be assumed to be induced if the path is induced. Motivated by these results, we consider the following problem: For a given class of graphs, determine all integers $\ell\geq 0$ such that for every graph in the class, e…

Quantum walks on finite and bounded infinite graphs
Chris Godsil, Steve Kirkland, Sarojini Mohapatra, Hermie Monterde, Hiranmoy Pal
https://arxiv.org/abs/2510.05306 https://

Quantum walks on finite and bounded infinite graphs
A weighted graph $G$ with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in $G$. In this paper, we prove a fundamental result on equitable partitions of bounded weighted graphs with twin subgraphs and use this fact to construct finite and bounded infinite graphs with pair and plus state transfer with the adjacency matrix as a Hamiltonian. We show that for each $k \ge 3$, (i) there are infinitely ma…

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 16726 nodes and 47594 edges.
Tags: Social, Collaboratio…

Spectral gap of $G(n, \alpha n, \alpha^2 n)$ graphs and the giant component theorem
M. Koshelev, A. Raigorodskii
https://arxiv.org/abs/2510.06722 https://a…

Spectral gap of $G(n, αn, α^2 n)$ graphs and the giant component theorem
The spectrum of a graph $G$ is the set of the eigenvalues of its adjacency matrix. It turns out that one can say a lot about a graph with the only knowledge being the spectrum of this graph. In this paper we obtain new results about the spectrum of $G(n, αn, α^2 n)$ graphs. We then apply these results to get a giant component theorem for them.

On the multiplicity of matching polynomial roots and $\theta$-critical graphs
Leyou Xu
https://arxiv.org/abs/2509.23842 https://arxiv.org/pdf/2509.23842

On the multiplicity of matching polynomial roots and $θ$-critical graphs
The matching polynomial of a graph encodes rich combinatorial information through its roots. We determine the maximum multiplicity of a non-zero matching polynomial root and characterize all graphs attaining the bound. We also generalize the result to any fixed $θ$, where the graphs attaining the bound are related to $θ$-critical graphs. Inspired by these graphs, we give a constructive answer to Godsil's question. Finally, we show the existence of $1$-critical tree of order $n$ for all $n\ge …

Zero Forcing, Leaky Zero Forcing, and Leaky Forts on Hopi Rectangle Graphs
Ryan Moruzzi Jr, Sagar Shah, Aaditeya Tripathi
https://arxiv.org/abs/2509.21529 https://

Zero Forcing, Leaky Zero Forcing, and Leaky Forts on Hopi Rectangle Graphs
We study the family of Hopi rectangle graphs, a planar generalization of the well-studied Aztec diamond graphs. We provide a new definition of this graph family as induced subgraphs of the Cartesian product of two path graphs, which helps frame our study. We then establish that the maximum nullity and the zero forcing number coincide for all Hopi rectangle graphs. Extending to the fault tolerant framework of leaky zero forcing, we use the notion of leaky forts to get a complete characterization…

Fractionally colouring $P_5$-free graphs
Tung H. Nguyen
https://arxiv.org/abs/2510.05724 https://arxiv.org/pdf/2510.05724

Fractionally colouring $P_5$-free graphs
We obtain some $d\ge2$ such that every graph $G$ with no induced copy of the five-vertex path $P_5$ has at most $α(G)ω(G)^d$ vertices. This ``off-diagonal Ramsey'' statement implies that every such graph $G$ has fractional chromatic number at most $ω(G)^d$, and is another step towards the polynomial Gyárfás-Sumner conjecture for $P_5$. The proof uses the recent Erdős-Hajnal result for $P_5$ and adapts a decomposition argument for $P_5$-free graphs developed by the author in an earlier pap…

The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs
Yair Caro, Mirko Petru\v{s}evski, Riste \v{S}krekovski, Zsolt Tuza
https://arxiv.org/abs/2510.01897

The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs
An odd independent set $S$ in a graph $G=(V,E)$ is an independent set of vertices such that, for every vertex $v \in V \setminus S$, either $N(v) \cap S = \emptyset$ or $|N(v) \cap S| \equiv 1$ (mod 2), where $N(v)$ stands for the open neighborhood of $v$. The largest cardinality of odd independent sets of a graph $G$, denoted $α_{od}(G)$, is called the odd independence number of $G$. This new parameter is a natural companion to the recently introduced strong odd chromatic number. …

Clique number of xor-powers of Kneser graphs
Zolt\'an F\"uredi, Andr\'as Imolay, \'Ad\'am Schweitzer
https://arxiv.org/abs/2510.01509 https://

Clique number of xor-powers of Kneser graphs
Let $f_\ell(n, k)$ denote the clique number of the xor-product of $\ell$ isomorphic Kneser graphs KG(n,k). Alon and Lubetzky investigated the case of complete graphs as a coding theory problem and showed $f_\ell(n,1)\leq \ell n +1$. Imolay, Kocsis, and Schweitzer proved that $f_2(n,k)\leq n/k +c(k)$. Here, the order of magnitude of $c(k)$ is determined to be $Θ\left( k \binom{2k}{k} \right)$. By explicit constructions and by an algebraic proof, it is shown that $\ell n- 2\ell-1 \leq f_\ell(n…

Competitively Constructed Planar Graphs
Wesley Pegden, Eric Wang
https://arxiv.org/abs/2510.01383 https://arxiv.org/pdf/2510.01383

Competitively Constructed Planar Graphs
We introduce and study two Maker-Breaker-like games for constructing planar graphs: the edge drawing game, where two players take turns drawing non-intersecting edges between points in the plane, and the circle packing game, where the players take turns placing disjoint circles in the plane. Both games produce planar graphs: the edge drawing game results in a plane graph drawing, and the circle packing game yields a planar graph via the contact graph of the packing. For both games, we give nece…

The high order spectral radius of graphs without long cycles or paths
Yuntian Wang, Lizhu Sun, Changjiang Bu
https://arxiv.org/abs/2510.04461 https://arxiv…

The high order spectral radius of graphs without long cycles or paths
In 1959, Erdős and Gallai established two classic theorems, which determine the maximum number of edges in an $n$-vertex graph with no cycles of length at least $k$, and in an $n$-vertex graph with no paths on $k$ vertices, respectively. Subsequently, generalized and spectral versions of the Erdős-Gallai theorems have been investigated. A concept of a high order spectral radius for graphs was introduced in 2023, defined as the spectral radius of a tensor and termed the $t$-clique spectral rad…

Discrete Curvatures and Convex Polytopes
Jes\'us A. De Loera, Jillian Eddy, Sawyer Jack Robertson, Jos\'e Alejandro Samper
https://arxiv.org/abs/2510.11894 https://

Discrete Curvatures and Convex Polytopes
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere positive curvature, and what structural constraints does positivity impose? For Forman--Ricci curvature we derive an exact identity for the average edge curvature in terms of flag $f$-numbers and establish the existence of infinite families of Forman--Ricci-positive polytopes in every fixed dimension $d\ge 6$. We prove fi…