arXiv subjects

Alexander Bastien

Publications and source records attributed to Alexander Bastien.

4 recordsLinked to original sources

arXiv2026

Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction

We present two approaches for predicting tennis match outcomes using topological data analysis and graph theory on ATP singles matches from 2000-2025. The first method applies lower-star filtration to player competitive networks, extracting topological features through persistent homology using four summary methods (VAB, HNAV, HWNAV, OW-HNPV) combined with Modified Band Depth analysis. Algorithmic optimizations including ego graph approximations and triangle elimination enable analysis of about 66k matches. Our Random Forest model achieves 66.2% accuracy (AUC = 0.719) using topological, graph-theoretic, and ranking features. Feature importance analysis reveals that rankings contribute 36.3%, centralities 25.5%, and TDA features 24.0%, with topological features providing complementary signal. When rankings are unavailable, the topology-only model maintains 63.56% accuracy, demonstrating that network-derived features alone capture meaningful competitive structure. The second method uses a modified Katz similarity index with temporal edge weighting, achieving 62.48% accuracy on held-out test data. This work represents the first application of lower-star filtration to tennis prediction, provides systematic comparison of four topological summary methods in sports analytics, and demonstrates that TDA can achieve above-chance prediction using network topology alone while providing additional value when combined with traditional features.

cs.LG↗

arXiv2025

On Link-irregular Digraphs

We extend the study of link-irregular graphs to directed graphs (digraphs), where a digraph is link-irregular if no two vertices have isomorphic directed links. We establish that link-irregular digraphs exist on $n$ vertices if and only if $n \geq 5$, and prove that their underlying graphs must contain 3-cycles. We conjecture that link-irregular tournaments exist if and only if $n \geq 6$, providing explicit constructions for $n \leq 8$ and computational verification for $n \leq 100$. We derive lower bounds on the minimum degree and outdegree required for link-irregularity, establish that almost all link-irregular digraphs are nonplanar, and prove that any link-irregular orientable graph admits a link-irregular labeling. Additionally, we construct explicit examples of link-irregular digraphs with constant outdegree and regular tournaments.

math.CO↗

arXiv2025

On Link-irregular labelings of Graphs

We introduce the concept of link-irregular labelings for graphs, extending the notion of link-irregular graphs through edge labeling with positive integers. A labeling is link-irregular if every vertex has a uniquely labeled subgraph induced by its neighbors. We establish necessary and sufficient conditions for the existence of such labelings and define the link-irregular labeling number $\eta(G)$ as the minimum number of distinct labels required. Our main results include necessary and sufficient conditions for the existence of link-irregular labelings. We show that certain families of graphs, such as bipartite graphs, trees, cycles, hypercubes, and complete multipartite graphs, do not admit link-irregular labelings, while complete graphs and wheel graphs do. Specifically, we prove that $\eta(K_n) = 2$ for $n \geq 6$ and $\eta(K_n) = 3$ for $n \in \{3,4,5\}$. For wheel graphs $W_n$, we establish that $\eta(W_n) \approx \sqrt{2n}$ asymptotically. Finally, we prove that for every positive integer $n$, there exists a graph with a link-irregular labeling number exactly $n$, and provide several results on graph operations that preserve labeling numbers.

math.CO↗

arXiv2025

On the Regularity, Planarity and Edge Bounds of Link-irregular Graphs

A graph $G$ is a link-irregular graph if every two distinct vertices of $G$ have non-isomorphic links. The link of a vertex $v$ in $G$ is the subgraph induced by the neighbors of $v$ in $G$. Ali, Chartrand and Zhang [Discussiones Mathematicae. Graph Theory, 45(1) (2025) p.95] conjectured that there exists no regular link-irregular graph. In this paper, we show that the existence of an $r$-regular link irregular graph is very likely for large enough $r$. In particular, we provide a 7-regular link irregular graph on 12 vertices, which serves as a counterexample to the conjecture. Additionally, we prove that no bipartite link-irregular graphs exist, and there are no regular link-irregular graphs on $n$-vertices for $n \leq 9$. Also, we determine upper and lower bounds for the number of edges of link-irregular graphs. Furthermore, we show the minimum number of edges in a link-irregular graph on the $n$ vertices is $\Omega(n\sqrt{\log n})$. Finally, we prove that all but finitely many link-irregular graphs are non-planar, and there is no regular link-irregular planar graphs.

math.CO↗