The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
LineMVGNN improves AML detection by integrating multi-view graph learning.
problem Ineffective and scalable AML systems using rule-based methods.
method LineMVGNN combines multi-view graph neural networks with line-graph features.
result LineMVGNN outperforms state-of-the-art methods in detecting money laundering.
Modern intelligent transportation systems provide data that allow real-time dynamic demand prediction, which is essential for planning and operations. The main challenge of prediction of dynamic Origin-Destination (O-D) demand matrices is that demands cannot be directly measured by traffic sensors; instead, they have t…
LG algorithm finds profitable trading paths in decentralized exchanges.
problem Identifying optimal trading paths in decentralized exchanges.
method Line-graph-based algorithm (LG) for efficient route discovery.
result LG consistently identifies more profitable paths than DFS with comparable costs.
A new algorithm tackles graph-based contextual bandits with efficient regret bounds.
problem Predicting labels on graphs with contextual bandit methods.
method Graph-based contextual bandit algorithm using optimal stochastic bandit techniques.
result Regret bounds for line graphs and trees, and improved bounds for general graphs.
Study classifies graphs with positive curvature without quadrilaterals.
problem Classifying graphs with positive Lin-Lu-Yau curvature without quadrilaterals.
method Definition of Ricci curvature on graphs, limit-free formulation using graph Laplacian.
result Identifies all simple connected C4-free graphs with positive Lin-Lu-Yau curvature.
Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thr…
This paper introduces STAP to measure DEX efficiency and shows better routing algorithms increase DEX performance and stakeholder benefits.
problem Measuring and improving the efficiency of decentralized exchanges (DEXs).
method Introduces STAP as a measure of DEX efficiency and compares two routing algorithms.
result Better routing algorithms improve DEX efficiency and stakeholder benefits.
New algorithm reduces regret in multi-agent bandits over undirected graphs.
problem Minimize regret in a multi-agent bandit setting with malicious agents.
method Proposed a new algorithm for undirected graphs, considering the number of malicious neighbors.
result The new algorithm achieves nearly linear regret improvement over existing methods.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
New algorithm finds more arbitrage opportunities in DEXs.
problem Detecting arbitrage loops and non-loops in decentralized exchanges.
method Combining line graph and modified Moore-Bellman-Ford algorithm.
result Found more arbitrage loops and non-loops compared to existing methods.
Generative model captures hubs and dense communities in social networks.
problem Capturing both hubs and dense communities in social networks.
method Graphon mixture model with a new condition on sparse graphs.
result Estimation of hub normalized degree and graphon for sparse components.
Graphs with maximum degree Δ have at most O(1) equiangular lines for λ < 3/sqrt(2).
problem Finding the maximum number of equiangular lines in graphs with a given maximum degree.
method Using eigenfunctions and nodal domains to estimate the multiplicity of eigenvalues.
result The maximum multiplicity of λ as the second largest eigenvalue is O(1) for graphs with maximum degree Δ and cyclomatic number.
In many video coding systems, separable transforms (such as two-dimensional DCT-2) have been used to code block residual signals obtained after prediction. This paper proposes a parametric approach to build graph-based separable transforms (GBSTs) for video coding. Specifically, a GBST is derived from a pair of line gr…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with…
We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs (DAGs), where nodes represent hypotheses and edges specify a partial ordering in which hypotheses must be tested. The procedure is guaranteed to reject a sub-DAG with bounded false discovery rate (FDR) while satisf…
The paper introduces curvature-based clustering algorithms for graph analysis.
problem Identifying densely connected substructures in graphs for community detection.
method Discrete Ricci curvatures and geometric flows to reveal community structure.
result The curvature-based approach can identify overlapping communities in graphs.
New hypergraph neural network learns variable-sized hyperedges.
problem Learning representations for non-uniform hypergraphs with variable cardinalities.
method Developed a hypergraph neural network exploiting incidence structure.
result Significant improvement in accuracy on real-world hypergraph datasets.
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks and for visualisation purposes. Whereas a large number of dedicated…
A simple method for estimating PMF on large supports, preserving structure and suppressing noise.
problem Nonparametric estimation of multi-modal, heavy-tailed PMF on large discrete support.
method Data-dependent low-pass filtering on a line graph Laplacian.
result Smooth, multi-modal estimate of PMF that preserves coarse structure and suppresses noise.
Simpler algorithms for morphing planar and toroidal graphs.
problem Constructing smooth transitions between isomorphic drawings of planar and toroidal graphs.
method Barycentric interpolation and scaling strategy.
result Simplified and more natural morphs with improved computational efficiency.
pLSTM tackles long-range language modeling and computer vision tasks with parallelizable linear source transition mark networks.
problem Challenges of existing recurrent architectures in handling sequences and multi-dimensional data.
method Introduces pLSTM, a parallelizable linear source transition mark network for linear graphs and DAGs, addressing vanishing/exploding activation/gradient issues.
result pLSTM outperforms Transformers in long-range tasks like arrow-pointing extrapolation and image size extrapolation.
New algorithms verify and search causal graphs with minimal interventions.
problem Recovering causal graphs from interventional data.
method Characterization of minimal intervention sets for verification, and adaptive graph separator algorithm for search.
result First provable algorithms for efficient verification and search of causal graphs.
Gauss-Bonnet for simple graphs G assures that the sum of curvatures K(x) over the vertex set V of G is the Euler characteristic X(G). Poincare-Hopf tells that for any injective function f on V the sum of i(f,x) is X(G). We also know that averaging the indices E[i(f,x)] over all functions gives curvature K(x). We explor…