arXiv subjects

Anthony Bonato

Publications and source records attributed to Anthony Bonato.

At least 19 recordsLinked to original sources

arXiv2026

Structural Change and Random Graph Models in Global Oil Trade Networks

We studied structural change in global oil trade using a network approach. Using UN Comtrade data, we examined the temporal evolution of international trade networks, with an emphasis on crude oil. Weighted in-degree identified major changes in country rankings in 1991, 2011, 2017, and 2021, while PageRank detected pronounced changes around 1991 and 2024. The Louvain algorithm identified clear geographic communities within the overall trade network. In the oil trade network, modularity declined from the 1990s to the 2010s, with node2vec embeddings showing weaker clustering in 2011 than in 1991. We also compared the oil trade network with several random graph models using 3- and 4-node subgraph profiles and machine learning classification. The oil trade network was consistently classified as a Chung-Lu graph, while the Geometric model was not favored, suggesting that a model based on the degree distribution better matched its subgraph profiles than the other models considered.

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arXiv2026

Cooling graph products

The cooling number measures the speed at which a slow-moving influence or contagion spreads on a graph. In this paper, we investigate the cooling number of four classical graph products: the Cartesian product, the strong product, the lexicographic product, and the direct product. We also determine the cooling number of a disconnected graph in terms of the cooling numbers of its components. We conclude with open problems.

math.CO↗

arXiv2026

Network analysis and link prediction in competitive women's basketball

Network structure and its role in prediction are examined in competitive basketball at the team and player levels. Adversarial game outcome networks from NCAA Division I women's basketball from 2021 to 2024 are used to compute the common out-neighbor score and PageRank, which are combined into a low-key leader strength that identifies competitors influential through structural similarity despite relatively low centrality. This measure is related to changes in NCAA NET rankings by grouping teams into quantiles and comparing average rank changes across seasons for both previous-to-current and current-to-next transitions. Link prediction is then studied using node2vec embeddings across three interaction settings. For NCAA regular-season game networks, cosine similarity between team embeddings is used in a logistic regression model to predict March Madness matchups. For WNBA shot-blocking networks, future directed blocking interactions are predicted via logistic regression on concatenated source-target player embeddings. For WNBA passing networks, region embeddings learned from first-quarter passes are evaluated for their ability to predict subsequent passing connections. Across NCAA and WNBA settings, embedding-based models provide statistically significant evidence that higher-order network structure contains predictive signals for future interactions, while the passing experiment shows weaker predictive performance but yields interpretable similarity patterns consistent with passing feasibility.

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arXiv2026

The Iterated Local Model for tournaments

Transitivity is a central, generative principle in social and other complex networks, capturing the tendency for two nodes with a common neighbor to form a direct connection. We propose a new model for highly dense, complex networks based on transitivity, called the Iterated Local Model Tournament (ILMT). In ILMT, we iteratively apply transitivity to form new tournaments by cloning nodes and their adjacencies, and either preserving or reversing the orientation of existing arcs between clones. The resulting model generates tournaments with small diameters and high connectivity as observed in real-world complex networks. We analyze subtournaments or motifs in the ILMT model and their universality properties. For many parameter choices, the model generates sequences of quasirandom tournaments. We also study the graph-theoretic properties of ILMT tournaments, including their cop number, domination number, and chromatic number. We finish with a set of open problems and variants of the ILMT model for oriented graphs.

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arXiv2025

Network Embedding Analysis for Anti-Money Laundering Detection

We employ network embedding to detect money laundering in financial transaction networks. Using real anonymized banking data, we model over one million accounts as a directed graph and use it to refine previously detected suspicious cycles with node2vec embeddings, creating a new network parameter, the spread number. Combined with more traditional centrality measures, these define an aggregate score $R$ that highlights so-called anti-central nodes: accounts that are structurally important yet organized to avoid detection. Our results show only a small subset of cycles attain high $R$ values, flagging concentrated groups of suspicious accounts. Our approach demonstrates the potential of embedding-based network analysis to expose laundering strategies that evade traditional graph centrality measures.

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arXiv2025

Between burning and cooling: liminal burning on graphs

Liminal burning generalizes both the burning and cooling processes in graphs. In $k$-liminal burning, a Saboteur reveals $k$-sets of vertices in each round, with the goal of extending the length of the game, and the Arsonist must choose sources only within these sets, with the goal of ending the game as soon as possible. The result is a two-player game with the corresponding optimization parameter called the $k$-liminal burning number. For $k = |V(G)|$, liminal burning is identical to burning, and for $k = 1$, liminal burning is identical to cooling. Using a variant of Sperner sets, $k$-liminal burning numbers of hypercubes are studied along with bounds and exact values for various values of $k$. In particular, we determine the exact cooling number of the $n$-dimensional hypercube to be $n.$ We analyze liminal burning for several graph families, such as Cartesian grids and products, paths, and graphs whose vertex sets can be decomposed into many components of small diameter. We consider the complexity of liminal burning and show that liminal burning a graph is PSPACE-complete for $k\geq 2,$ using a reduction from $3$-QBF. We also prove, through a reduction from burning, that even in some cases when liminal burning is likely not PSPACE-complete, it is co-NP-hard. We finish with several open problems.

math.CO↗

arXiv2025

Network Analysis of Global Banking Systems and Detection of Suspicious Transactions

A novel network-based approach is introduced to analyze banking systems, focusing on two main themes: identifying influential nodes within global banking networks using Bank for International Settlements data and developing an algorithm to detect suspicious transactions for anti-money laundering. Leveraging the concept of adversarial networks, we examine Bank for International Settlements data to characterize low-key leaders and highly-exposed nodes in the context of financial contagion among countries. Low-key leaders are nodes with significant influence despite lower centrality, while highly-exposed nodes represent those most vulnerable to defaults. Separately, using anonymized transaction data from Rabobank, we design an anti-money laundering algorithm based on network partitioning via the Louvain method and cycle detection, identifying unreported transaction patterns indicative of potential money laundering. The findings provide insights into system-wide vulnerabilities and propose tools to address challenges in financial stability and regulatory compliance.

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arXiv2025

Analysis and predictability of centrality measures in competition networks

The Common Out-Neighbor (or CON) score quantifies shared influence through outgoing links in competitive contexts. A dynamic analysis of competition networks reveals the CON score as a powerful predictor of node rankings. Defined in first-order and second-order forms, the CON score captures both direct and indirect competitive interactions, offering a comprehensive metric for evaluating node influence. Using datasets from Survivor, Chess.com, and Dota~2 online gaming competitions, directed competition networks are constructed, and the dynamic CON score is integrated into supervised machine learning models. Empirical results show that the CON score consistently outperforms traditional centrality measures such as PageRank, closeness, and betweenness centrality in classification tasks. By integrating dynamic centrality measures with machine learning, our proposed methodology accurately predicts outcomes in competition networks. The findings underline the CON score's robustness as a feature in node classification, offering a significant advancement in understanding and analyzing competitive interactions.

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arXiv2024

Hypergraph burning, matchings, and zero forcing

Lazy burning is a recently introduced variation of burning where only one set of vertices is chosen to burn in the first round. In hypergraphs, lazy burning spreads when all but one vertex in a hyperedge is burned. The lazy burning number is the minimum number of initially burned vertices that eventually burns all vertices. We give several equivalent characterizations of lazy burning on hypergraphs using matchings and zero forcing, and then apply these to give new bounds and complexity results. We prove that the lazy burning number of a hypergraph $H$ equals its order minus the maximum cardinality of a certain matching on its incidence graph. Using this characterization, we give a formula for the lazy burning number of a dual hypergraph and give new bounds on the lazy burning number based on various hypergraph parameters. We show that the lazy burning number of a hypergraph may be characterized by a maximal subhypergraph that results from iteratively deleting vertices in singleton hyperedges. We prove that lazy burning on a hypergraph is equivalent to zero forcing on its incidence graph and show an equivalence between skew zero forcing on a graph and lazy burning on its neighborhood hypergraph. As a result, we show that finding an upper bound on the lazy burning number of a hypergraph is NP-complete, which resolves a conjecture from \cite{BJR}. By applying lazy burning, we show that computing an upper bound on the skew zero forcing number for bipartite graphs is NP-complete. We finish with open problems.

math.CO↗

arXiv2024

Enhancing Anti-Money Laundering Efforts with Network-Based Algorithms

The global banking system has faced increasing challenges in combating money laundering, necessitating advanced methods for detecting suspicious transactions. Anti-money laundering (or AML) approaches have often relied on predefined thresholds and machine learning algorithms using flagged transaction data, which are limited by the availability and accuracy of existing datasets. In this paper, we introduce a novel algorithm that leverages network analysis to detect potential money laundering activities within large-scale transaction data. Utilizing an anonymized transactional dataset from Co\"operatieve Rabobank U.A., our method combines community detection via the Louvain algorithm and small cycle detection to identify suspicious transaction patterns below the regulatory reporting thresholds. Our approach successfully identifies cycles of transactions that may indicate layering steps in money laundering, providing a valuable tool for financial institutions to enhance their AML efforts. The results suggest the efficacy of our algorithm in pinpointing potentially illicit activities that evade current detection methods.

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arXiv2024

How to burn a Latin square

We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that burning spreads to neighboring vertices over time via a specified propagation rule. The lazy burning number is the minimum number of initially burned vertices that eventually burns all vertices. The hypergraphs associated with Latin squares include the $n$-uniform hypergraph, whose vertices and hyperedges correspond to the entries and lines (that is, sets of rows, columns, or symbols) of the Latin square, respectively, and the $3$-uniform hypergraph, which has vertices corresponding to the lines of the Latin square and hyperedges induced by its entries. Using sequences of vertices that together form a vertex cover, we show that for a Latin square of order $n$, the lazy burning number of its $n$-uniform hypergraph is bounded below by $n^2-3n+3$ and above by $n^2-3n+2 + \lfloor \log_2 n \rfloor.$ These bounds are shown to be tight using cyclic Latin squares and powers of intercalates. For the $3$-uniform hypergraph case, we show that the lazy burning number of Latin squares is one plus its shortest connected chain of subsquares. We determine the lazy burning number of Latin square hypergraphs derived from finitely generated groups. We finish with open problems.

math.CO↗

arXiv2024

The isoperimetric peak of complete trees

We give exact values and bounds on the isoperimetric peak of complete trees, improving on known results. For the complete $q$-ary tree of depth $d$, if $q\ge 5$, then we find that the isoperimetric peak equals $d$, completing an open problem. In the case that $q$ is 3 or 4, we determine the value up to three values, and in the case $q=2$, up to a logarithmic additive factor. Our proofs use novel compression techniques, including left, down, and aeolian compressions. We apply our results to show that the vertex separation number and the isoperimetric peak of a graph may be arbitrarily far apart as a function of the order of the graph and give new bounds on the pathwidth and pursuit-evasion parameters on complete trees.

math.CO↗

arXiv2024

Locally finite graphs and their localization numbers

We study the Localization game on locally finite graphs trees, where each of the countably many vertices have finite degree. In contrast to the finite case, we construct a locally finite tree with localization number $n$ for any choice of positive integer $n$. Our examples have uncountably many ends, and we show that this is necessary by proving that locally finite trees with finitely or countably many ends have localization number at most 2. Finally, as is the case for finite graphs, we prove that any locally finite graph contains a subdivision where one cop can capture the robber.

math.CO↗

arXiv2024

How to cool a graph

We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures the speed of a slow-moving contagion in a graph; the lower the cooling number, the faster the contagion spreads. We provide tight bounds on the cooling number via a graph's order and diameter. Using isoperimetric results, we derive the cooling number of Cartesian grids. The cooling number is studied in graphs generated by the Iterated Local Transitivity model for social networks. We conclude with open problems.

math.CO↗

arXiv2024

Clique counts for network similarity

Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in graphlet counts as a method for graph similarity in social networks. Higher-order clustering coefficients and the Pivoter algorithm for exact clique counts are employed

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arXiv2023

The $k$-visibility Localization Game

We study a variant of the Localization game in which the cops have limited visibility, along with the corresponding optimization parameter, the $k$-visibility localization number $ζ_k$, where $k$ is a non-negative integer. We give bounds on $k$-visibility localization numbers related to domination, maximum degree, and isoperimetric inequalities. For all $k$, we give a family of trees with unbounded $ζ_k$ values. Extending results known for the localization number, we show that for $k\geq 2$, every tree contains a subdivision with $ζ_k = 1$. For many $n$, we give the exact value of $ζ_k$ for the $n \times n$ Cartesian grid graphs, with the remaining cases being one of two values as long as $n$ is sufficiently large. These examples also illustrate that $ζ_i \neq ζ_j$ for all distinct choices of $i$ and $j.$

math.CO↗

arXiv2023

The Iterated Local Transitivity Model for Tournaments

A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local Transitivity Tournament (or ILTT) model. In ILTT and a dual version of the model, we iteratively apply the principle of transitivity to form new tournaments. The resulting models generate tournaments with small average distances as observed in real-world complex networks. We explore properties of small subtournaments or motifs in the ILTT model and study its graph-theoretic properties, such as Hamilton cycles, spectral properties, and domination numbers. We finish with a set of open problems and the next steps for the ILTT model.

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arXiv2023

The one-visibility Localization game

We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the one-visibility localization number $\zeta_1$. By developing lower bounds using isoperimetric inequalities, we give upper and lower bounds for $\zeta_1$ on $k$-ary trees with $k\ge 2$ that differ by a multiplicative constant, showing that the parameter is unbounded on $k$-ary trees. We provide a $O(\sqrt{n})$ bound for $K_h$-minor free graphs of order $n$, and we show Cartesian grids meet this bound by determining their one-visibility localization number up to four values. We present upper bounds on $\zeta_1$ using pathwidth and the domination number and give upper bounds on trees via their depth and order. We conclude with open problems.

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