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Multiscale Graph Comparison via the Embedded Laplacian Discrepancy
[article]
2023
arXiv
pre-print
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The use of Laplacian eigenvectors as embeddings for the purpose of multiscale graph comparison has however been limited. ...
Here we propose the Embedded Laplacian Discrepancy (ELD) as a simple and fast approach to compare graphs (of potentially different sizes) based on the similarity of the graphs' community structures. ...
It suffices that we show the empirical measure of a graph is invariant under sign configurations of eigenvectors. Pick an arbitary eigenvector v 𝑟 from either graph for any 1 ≤ 𝑟 ≤ 𝑘. ...
arXiv:2201.12064v2
fatcat:vznzphhvqneuhmlojlcrzn2uwi
Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning
[article]
2021
arXiv
pre-print
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In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data. ...
We demonstrate the effectiveness of our proposed model on various graph reconstruction and generation tasks and evaluate the expressive power of extracted representations for downstream graph-level classification ...
To break symmetry and inject information about the relative position/order of nodes to each other, we follow [18] and define position embeddings in dimension k PE(i) k = sin(i/10000 2k/dz ), for even ...
arXiv:2104.09856v2
fatcat:dcmxbft6hrbxpmjpkn4fdovzfu
Graph Random Neural Features for Distance-Preserving Graph Representations
[article]
2020
arXiv
pre-print
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The embedding naturally deals with graph isomorphism and preserves the metric structure of the graph domain, in probability. ...
We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. ...
Acknowledgements This research is funded by the Swiss National Science Foundation project 200021 172671: "ALPSFORT: A Learning graPh-baSed framework FOr cybeR-physical sysTems." The work of L. ...
arXiv:1909.03790v3
fatcat:2eink7sbbrhhdjsmnuszm3kd7e
Expectation-Complete Graph Representations with Homomorphisms
[article]
2023
arXiv
pre-print
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2023 pre-print arXiv:2306.05838v1 fatcat:i7q7i5excnfgrmwur53donz5i4
Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. ...
Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. ...
of North Rhine-Westphalia as part of the Lamarr Institute for Machine Learning and Artificial Intelligence, LAMARR22B. ...
arXiv:2306.05838v2
fatcat:o2ijn63vdjdndg2d2qjblgi6m4
Reduced Wu and generalized Simon invariants for spatial graphs
2014
Mathematical proceedings of the Cambridge Philosophical Society (Print)
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crossing number of embedded graphs. ...
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal ...
The authors are grateful to Professor Kouki Taniyama for suggesting that the Wu invariant might be used to obtain bounds on the minimal crossing number of a spatial graph. ...
doi:10.1017/s0305004114000073
fatcat:aug62oeo5ncglaif4hcfceyl7a
Persistent Homology and Graphs Representation Learning
[article]
2021
arXiv
pre-print
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This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. ...
Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. ...
For instance, one may simply add all node embeddings of a given graph to obtain a graph descriptor. ...
arXiv:2102.12926v4
fatcat:q6o32m6eejapbdpnmqk54wspvm
Shape-Based Retrieval of Articulated 3D Models Using Spectral Embedding
[chapter]
2006
Lecture Notes in Computer Science
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We represent each shape by the eigenvectors of an appropriately defined affinity matrix, obtaining a spectral embedding. ...
We present an approach for robust shape retrieval from databases containing articulated 3D shapes. ...
Construction of structural graph: We use shortest graph distances over a mesh graph to approximate geodesic distances. ...
doi:10.1007/11802914_21
fatcat:jainna2fszddrjbx77bpsjomci
AlignGraph: A Group of Generative Models for Graphs
[article]
2023
arXiv
pre-print
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It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is ...
We propose AlignGraph, a group of generative models that combine fast and efficient graph alignment methods with a family of deep generative models that are invariant to node permutations. ...
Since Â0 j,k ∈ [0, 1], ∀j, k ∈ [m], we binarize the elements of the adjacency matrix for G 0 by using a threshold. ...
arXiv:2301.11273v1
fatcat:2ap6nch3ibe27d3uafqpxumymu
Graph invariants from ideas in physics and number theory
[article]
2015
arXiv
pre-print
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We complement this invariant by another type of graph invariants, coming from viewing graphs as quadratic forms over the integers. ...
We show that this gives rise to a graph invariant, which is closely related to the 2-dim Weisfeiler-Lehman algorithm for graph isomorphism testing. ...
For instance, the pair of graphs in K (−4) 6 with distance 1.2674, shown in Figure 5 , are of the same degree of vertices (3, 3, 4, 4, 4, 4) ; the pair of graphs in K (−6) 7 with distance 0.2750, shown ...
arXiv:1409.5853v3
fatcat:l5ebln7i4zbbzmmrqtg6vgwmze
Graph Characteristic from the Gauss-Bonnet Theorem
[chapter]
2008
Lecture Notes in Computer Science
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We commence by embedding the nodes of a graph in a manifold using the heat-kernel mapping. ...
From this mapping we are able to compute the geodesic and Euclidean distance between nodes, and these can be used to estimate the sectional curvatures of edges. ...
Although the spectrum of a graph (i.e. the set of eigenvalues of the Laplacian matrix) is a global permutation invariant characterisation, the set of eigenvectors are not permutation invariant and can ...
doi:10.1007/978-3-540-89689-0_25
fatcat:oyzt53e375eshamnfmc5zdecai
An embedding-based distance for temporal graphs
[article]
2024
arXiv
pre-print
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We define a distance between temporal graphs based on graph embeddings built using time-respecting random walks. ...
Leveraging state-of-the-art machine learning techniques, we propose an efficient implementation of distance computation that is viable for large-scale temporal graphs. ...
Acknowledgments LD and CC acknowledge support from the Lagrange Project of the ISI Foundation funded by CRT Foundation and from Fondation Botnar (EPFL COVID-19 Real Time Epidemiology I-DAIR Pathfinder) ...
arXiv:2401.12843v1
fatcat:sfrknvliyrbehl3leeiisblahy
Page 1707 of Mathematical Reviews Vol. , Issue 88d
[page]
1988
Mathematical Reviews
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(iii) optimal embeddings for various families of graphs. ...
1707
of the minimal subtree containing v and the vertices of S whose distance from v is at most d}. For r>0 let N(v,r) denote the set of vertices in V whose distance from v is at most r. ...
Heterogeneous Graph Matching Networks
[article]
2019
arXiv
pre-print
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invariant graph modeling of the program's execution behaviors. ...
To address the limitations of existing techniques, we propose MatchGNet, a heterogeneous Graph Matching Network model to learn the graph representation and similarity metric simultaneously based on the ...
Recently, a very promising means for studying complex systems has emerged through the concept of invariant graph [Cheng et al., 2016; . ...
arXiv:1910.08074v1
fatcat:hgqew4qbwzfvppiy53vsgeynyu
A Wasserstein Graph Distance Based on Distributions of Probabilistic Node Embeddings
[article]
2024
arXiv
pre-print
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Distance measures between graphs are important primitives for a variety of learning tasks. ...
Our idea is to derive representations of graphs as Gaussian mixture models, fitted to distributions of sampled node embeddings over the same space. ...
Due to the sorting, this embedding is invariant under isomorphism, that is, the probability of sampling a certain embedding is independent of the node ordering of the graph. ...
arXiv:2401.03913v2
fatcat:yxhkffmxvrcoddojcxubwiwmjq
Page 5974 of Mathematical Reviews Vol. , Issue 2004h
[page]
2004
Mathematical Reviews
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An /-topological embedding of K into H is a one-to-one mapping yp: V(K) — V(#) along with a set QO of paths in H, each of length </, such that for each edge wv € E(K) there is a corresponding path between ...
Then the /-distance between H and K, denoted by d/(H,K), is the sum e!(K, H) +e! (H,K).
Let %,, denote the set of all simple connected graphs of order n. The authors show that (F,,d!) ...
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