21 papers · ranked by Valyu relevance
C. B. Scott, Eric Mjolsness, Gabriele Oliva
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian…
Teddy Mishura
The space of L p graphons, symmetric measurable functions w : [0, 1]2 → R with finite p-norm, features heavily in the study of sparse graph limit theory. We show that the triangular cut operator Mχ acting on this space is not continuous with respect to the cut norm. This is achieved by showing that as n → ∞, the norm…
Svante Janson
We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show that the model can produce dense, sparse and extremely sparse random graphs.…
Christian Bick, Davide Sclosa
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems…
Cédric Simal, Julien Petit, Timoteo Carletti
We define an analogue of the shortest-path distance for graphons. The proposed method is rooted on the extension to graphons of Varadhan's formula, a result that links the solution of the heat equation on a Riemannian manifold to its geodesic distance. The resulting metric is integer-valued, and for step graphons…
Gábor Elek
Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in computer science in the context of testability of graph properties. In this paper we propose a unified approach to…
Garrison Koch, Nathan Shank
The Roman Dominating number is a widely studied variant of the dominating number on graphs. Given a graph G = (V, E), the dominating number of a graph is the minimum size of a vertex set, V ′ ⊆ V , so that every vertex in the graph is either in V ′ or is adjacent to a vertex in V ′ . A Roman Dominating function of G is…
Hamed Hatami, László Lovász, Balázs Szegedy
The colored neighborhood metric for sparse graphs was introduced by Bollob´as and Riordan [8]. The corresponding convergence notion refines a convergence notion introduced by Benjamini and Schramm [6]. We prove that even in this refined sense, the limit of a convergent graph sequence (with uniformly bounded degree) can…
Dorottya Beringer, Ádám Timár
There is an important parameter in control theory which is closely related to the directed matching ratio of the network, as shown in the paper of Liu et al. (Nature 473:167-173, [10]). We give proofs of two main statements of Liu et al. ([10]) on the directed matching ratio, which were based on numerical results and…
Laura Eslava, Sayle Sigarreta Ricardo, Arno Siri-Jégousse
We prove that the generalized Randić index over graphs following the Erdos-Rényi model, for both the sparse and dense regimes, is concentrated around its mean when the number of vertices tends to infinity.
Madhumangal Pal
| Annals of | | | |:-----|:--------------|:--------------| | Pure and Applied | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics | | | | Mathematics |…
Vignesh Prabhakar, Chau Vu, Jennifer Crawford, Joseph Waite + 1 more
Generating knowledge graph embeddings (KGEs) to represent entities (nodes) and relations (edges) in large scale knowledge graph datasets has been a challenging problem in representation learning. This is primarily because the embeddings / vector representations that are required to encode the full scope of data in a…
Authors not listed
Genetic Algorithms are a powerful method to solve optimization problems with complex cost functions over vast search spaces that rely in particular on recombining parts of previous solutions. Crossover operators play a crucial role in this context. Here, we describe a large class of these operators designed for…
Peter Wills, François G. Meyer
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience [1], cyber security [2], social network analysis [3], and bioinformatics [4], among others. Discovery and comparison of structures such as modular communities, rich clubs…
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenomena concerning geodesics arise due to inhomogeneity. These include novel Busemann functions associated with flat regions of the limit shape…
Authors not listed
We present a unified, set–theoretic framework that extends molecular graphs to hypergraphs and superhypergraphs via iterated power sets. We define Molecular Graphs, Molecular HyperGraphs, and Molecular SuperHyperGraphs, and develop four complements over them: Weighted, Rough, Neural, and Multipolar frameworks. We prove…
Maliheh Miri, Vahid Abootalebi, Hamid Saeedi-Sourck, Dimitri Van De Ville + 1 more
Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organization of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines within the setting of brain-computer interface systems as well as cognitive…
Xiaoxiao Li, Yuan Zhou, Siyuan Gao, Nicha Dvornek + 7 more
Understanding how certain brain regions relate to a specific neurological disorder or cognitive stimuli has been an important area of neuroimaging research. We propose BrainGNN, a graph neural network (GNN) framework to analyze functional magnetic resonance images (fMRI) and discover neurological biomarkers. In…
Haotian Li
Machine learning and deep learning are novel and trending approaches to solving real-world scientific problems. Graph machine learning is dedicated to performing learning methods, such as graph neural networks, on non-Euclidean data such as graphs. Molecules, with their natural graph structures, could be analyzed by…
David Buterez, Jon Paul Janet, Steven Kiddle, Pietro Liò
We investigate the potential of graph neural networks for transfer learning and improving molecular property prediction on sparse and expensive to acquire high-fidelity data by leveraging low-fidelity measurements as an inexpensive proxy for a targeted property ofinterest. This problem arises in discovery processes…
Authors not listed
Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…