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…

Zeta functions of abstract isogeny graphs and modular curves
Jun Bo Lau, Travis Morrison, Eli Orvis, Gabrielle Scullard, Lukas Zobernig
https://arxiv.org/abs/2509.15214 https://…

Zeta functions of abstract isogeny graphs and modular curves
We introduce a ``non-orientable'' variation of Serre's definition of a graph, which we call an abstract isogeny graph. These objects capture the combinatorics of the graphs $G(p,\ell,H)$, the $\ell$-isogeny graphs of supersingular elliptic curves with $H$-level structure. In particular they allow for the study of non-backtracking walks, primes, and zeta functions. We prove an analogue of Ihara's determinant formula for the zeta function of an abstract isogeny graph. For $B_1(N) \subseteq H \sub…

Ideally Connected Cographs and Chordal Graphs
Richter Jordaan
https://arxiv.org/abs/2509.14393 https://arxiv.org/pdf/2509.14393

Ideally Connected Cographs and Chordal Graphs
For distinct vertices $u,v$ in a graph $G$, let $κ_G(u,v)$ denote the maximum number of internally disjoint $u$-$v$ paths in $G$. Then, $κ_G(u,v) \leq \min\{ \mbox{deg}_G(u), \mbox{deg}_G(v) \}$. If equality is attained for every pair of vertices in $G$, then $G$ is called ideally connected. In this paper, we characterize the ideally connected graphs in two well-known graph classes: the cographs and the chordal graphs. We show that the ideally connected cographs are precisely the $2K_2$-free …

Scattering for time periodic Hamiltonians on graphs
Hiroshi Isozaki, Evgeny, L. Korotyaev
https://arxiv.org/abs/2509.14719 https://arxiv.org/pdf/2509.1471…

Scattering for time periodic Hamiltonians on graphs
We develop a scattering theory for time-periodic Hamiltonians on discrete graphs, including long-range potentials with zero average for the period, and show the existence and completeness of wave operators.

Existence, asymptotic behaviors, and high-dimensional uniqueness of topological solutions to the skew-symmetric Chern-Simons system on lattice graphs
Honggang Liu
https://arxiv.org/abs/2509.14538

Existence, asymptotic behaviors, and high-dimensional uniqueness of topological solutions to the skew-symmetric Chern-Simons system on lattice graphs
In this paper, we consider the topological solutions to the skew-symmetric Chern-Simons system on lattice graphs: $$\left\{\begin{aligned} Δu &=λ\mathrm{e}^{\upsilon}(\mathrm{e}^{u}-1)+4π\sum\limits_{j=1}^{k_1}m_jδ_{p_j}, Δ\upsilon&=λ\mathrm{e}^{u}(\mathrm{e}^{\upsilon}-1)+4π\sum\limits_{j=1}^{k_2}n_jδ_{q_j}, \end{aligned} \right. $$ here, $λ\in\mathbb{R}_+$, $k_1$ and $k_2$ are two positive integers, $m_j\in\mathbb{N}\, (j=1,2,\cdot\cdot\cdot,k_1)$, $n_j\in\mathbb{N}\,(j=1,2,\cdot\cdo…

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

Homological torsion growth in non-normal chains of graphs of free groups
Dario Ascari, Jonathan Fruchter
https://arxiv.org/abs/2509.15075 https://arxiv.org…

Homological torsion growth in non-normal chains of graphs of free groups
Let $G$ be a hyperbolic group that splits as a graph of free groups with cyclic edge groups, and which is not isomorphic to a free product of free and surface groups. We show that $G$ admits an exhausting, nested sequence of finite-index non-normal subgroups $G\ge G_1 \ge G_2 \ge \cdots$ with exponential homological torsion growth. More specifically, we prove that simultaneously for every prime $p$, $\liminf_{n\rightarrow \infty} \frac{\log \vert \mathrm{Tor}_p(G_n^{\mathrm{ab}})\vert}{[G:G_n]}…

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 22706 nodes and 92826 edges.
Tags: Technological, Communication, Unweighted, Temporal

Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs
Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
https://arxiv.org/abs/2509.15080

Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open problem was raised: whether the minimum sum coloring problem with bundles could be solved in polynomial time for trees. We answer their question in the negative by proving that the minimum sum coloring problem with bundles is NP-hard even for paths. We compl…

Componentwise linearity of powers of edge ideals of weighted oriented graphs
Manohar Kumar, Joydip Mondal, Ramakrishna Nanduri
https://arxiv.org/abs/2509.14637 https://

Componentwise linearity of powers of edge ideals of weighted oriented graphs
In this paper, we study the componentwise linearity of powers of edge ideal of a weighted oriented graph $D$. We give a characterization for componentwise linearity of the edge ideal $I(D)$ in terms of forbidden subgraphs of $D$. If $D$ is house-free or complete $r$-partite, then the following statements are equivalent: (1) $I(D)$ is componentwise linear; (2) $I(D)$ is vertex splittable; (3) $I(D)$ has linear quotient property; (4) both $G$ and $H(I(D)_{(2)})$ are co-chordal and $D_1,D_2,D_3,D…

Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles
Filip Naudot, Andreas Br\"annstr\"om, Vicen\c{c} Torra, Timotheus Kampik
https://arxiv.org/abs/2509.14963

Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles
We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations of existing functions that quantify the contribution of a single contributing argument to a topic. Accordingly, we generalize existing contribution function principles for set contribution functions and provide a corresponding principle-based analysis. We in…

Brain-HGCN: A Hyperbolic Graph Convolutional Network for Brain Functional Network Analysis
Junhao Jia, Yunyou Liu, Cheng Yang, Yifei Sun, Feiwei Qin, Changmiao Wang, Yong Peng
https://arxiv.org/abs/2509.14965

Brain-HGCN: A Hyperbolic Graph Convolutional Network for Brain Functional Network Analysis
Functional magnetic resonance imaging (fMRI) provides a powerful non-invasive window into the brain's functional organization by generating complex functional networks, typically modeled as graphs. These brain networks exhibit a hierarchical topology that is crucial for cognitive processing. However, due to inherent spatial constraints, standard Euclidean GNNs struggle to represent these hierarchical structures without high distortion, limiting their clinical performance. To address this limita…

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

On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Meike Wei{\ss}, Reymond Akpanya, Alice C. Niemeyer
https://arxiv.org/abs/2509.14964 https:/…

On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Although the strong embedding of a 3-connected planar graph $G$ on the sphere is unique, $G$ can have different inequivalent strong embeddings on a surface of positive genus. If $G$ is cubic, then the strong embeddings of $G$ on the projective plane, the torus and the Klein bottle each are in one-to-one correspondence with certain subgraphs of the dual graph $G^\ast$. Here, we exploit this characterisation and show that two strong embeddings of $G$ on the projective plane, the torus or the Klei…

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…

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 3752 nodes and 7449 edges.
Tags: Technological, Communication, Unweighted, Temporal

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…

Fast and Compact Sketch-Based Dynamic Connectivity
Quinten De Man, Qamber Jafri, Daniel Delayo, Evan T. West, Michael A. Bender, David Tench
https://arxiv.org/abs/2509.14433 htt…

Fast and Compact Sketch-Based Dynamic Connectivity
We study the dynamic connectivity problem for massive, dense graphs. Our goal is to build a system for dense graphs that simultaneously answers connectivity queries quickly, maintains a fast update throughput, and a uses a small amount of memory. Existing systems at best achieve two of these three performance goals at once. We present a parallel dynamic connectivity algorithm using graph sketching techniques that has space complexity $O(V \log^3 V)$ and query complexity $O(\log V/\log\log V)$…

Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs
Tuan Anh Dao, Anh Tuan Duong
https://arxiv.org/abs/2509.14767 https://

Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs
In this article, we are interested in studying the Cauchy problems for nonlinear damped wave equations and their systems on a weighted graph. Our main purpose is two-fold, namely, under certain conditions for volume growth of a ball and the initial data we would like to not only prove nonexistence of global (in time) weak solutions but also indicate lifespan estimates for local (in time) weak solutions when a blow-up phenomenon in finite time occurs. Throughout the present paper, we will partia…

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

Computing fault-tolerant metric dimension of graphs using their primary subgraphs
S. Prabhu, Sandi Klav\v{z}ar, K. Bharani Dharan, S. Radha
https://arxiv.org/abs/2509.14300 http…

Computing fault-tolerant metric dimension of graphs using their primary subgraphs
The metric dimension of a graph is the cardinality of a minimum resolving set, which is the set of vertices such that the distance representations of every vertex with respect to that set are unique. A fault-tolerant metric basis is a resolving set with a minimum cardinality that continues to resolve the graph even after the removal of any one of its vertices. The fault-tolerant metric dimension is the cardinality of such a fault-tolerant metric basis. In this article, we investigate the fault-…

Crosslisted article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Meike Wei{\ss}, Reymond Akpanya, Alice C. Niemeyer

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…

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…

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

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 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…

On Laplacian and Signless Laplacian Permanental Polynomials of Some Well-known Graphs
Sarbari Mitra, Soumya Bhoumik
https://arxiv.org/abs/2509.14389 https://

On Laplacian and Signless Laplacian Permanental Polynomials of Some Well-known Graphs
The permanent of an $n \times n$ matrix $M = (m_{ij})$ is defined as $\mathrm{per}(M) = \sum_{σ\in S_n} \prod_{i=1}^n m_{i,σ(i)}$, where $S_n$ denotes the symmetric group on $\{1,2,\ldots,n\}$. The permanental polynomial of $M$, is defined by $ψ(M;x) = \mathrm{per}(xI_n - M)$. We study two fundamental variants: the Laplacian permanental polynomial $ψ(L(G);x)$ and signless Laplacian permanental polynomial $ψ(Q(G);x)$ of a graph $G$. A graph is said to be {determined} by its (signless) Lapla…

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…

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…

Replaced article(s) found for math.SP. https://arxiv.org/list/math.SP/new
[1/1]:
- On a magneto-spectral invariant on finite graphs
Chunyang Hu, Bobo Hua, Supanat Kamtue, Shiping Liu, Florentin M\"unch, Norbert Peyerimhoff

Efficient Algorithms for Disjoint Shortest Paths Problem and its Extensions
Keerti Choudhary, Amit Kumar, Lakshay Saggi
https://arxiv.org/abs/2509.14588 https://

Efficient Algorithms for Disjoint Shortest Paths Problem and its Extensions
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent advances in disjoint shortest paths for DAGs and undirected graphs (Akmal et al. 2024), we present an $O(mn \log n)$ time algorithm for this problem in weighted directed graphs that do not contain negative or zero weight cycles. This algorithm presents a signif…

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

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

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 $q^2$ …

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

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,…

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…

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

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…

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…

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.

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

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…

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…

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…

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…

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

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…

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…

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…

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…

Spectra of Corona Products of Digraphs
Michael Cavers, Farzad Maghsoudi, Babak Miraftab
https://arxiv.org/abs/2509.14481 https://arxiv.org/pdf/2509.14481…

Spectra of Corona Products of Digraphs
Two types of corona products for simple directed graphs are introduced, extending the classical notions from the undirected setting: the vertex-corona and the arc-corona. Their structural and spectral properties are investigated through the use of digraph coronals, with particular emphasis on the adjacency, Laplacian, and signless Laplacian spectra. Finally, the coronals corresponding to these three matrices are computed for several families of digraphs.

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…

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.

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

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

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 …

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…

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…

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 …

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…

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…

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.

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

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…

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

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…

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…

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…

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…

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

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…

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…

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 …

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

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…

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…

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…

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…

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…

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 433 nodes and 1941 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…

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

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 334 nodes and 32988 edges.
Tags: Informational, Web gr…

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…

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…

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…

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…

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 …