Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data

Benson, Austin R.; Gleich, David F.; Higham, Desmond J.

doi:10.48550/arxiv.2103.05031

Cited by 5 publications

(6 citation statements)

References 30 publications

(32 reference statements)

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“…Problem Statement and Research Gap The works above provide the background for the generalization of graph neural networks to higher-order De Bruijn graph models of causal walks in dynamic graphs, which we propose in the following section. Following the terminology in the network science community, higher-order De Bruijn graph models can be seen as one particular type of higher-order network models [13,23,24], which capture (causally-ordered) sequences of interactions between more than two nodes, rather than dyadic edges. They complement other types of popular higher-order network models (like, e.g.…”

Section: Non-markovian Characteristics Of Dynamic Graphsmentioning

confidence: 99%

De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs

Qarkaxhija¹,

Perri²,

Scholtes³

2022

Preprint

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We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware graph neural network architecture for time-resolved data on dynamic graphs. Our approach accounts for temporal-topological patterns that unfold in the causal topology of dynamic graphs, which is determined by causal walks, i.e. temporally ordered sequences of links by which nodes can influence each other over time. Our architecture builds on multiple layers of higher-order De Bruijn graphs, an iterative line graph construction where nodes in a De Bruijn graph of order k represent walks of length k − 1, while edges represent walks of length k. We develop a graph neural network architecture that utilizes De Bruijn graphs to implement a message passing scheme that follows a non-Markovian dynamics, which enables us to learn patterns in the causal topology of a dynamic graph. Addressing the issue that De Bruijn graphs with different orders k can be used to model the same data set, we further apply statistical model selection to determine the optimal graph topology to be used for message passing. An evaluation in synthetic and empirical data sets suggests that DBGNNs can leverage temporal patterns in dynamic graphs, which substantially improves the performance in a supervised node classification task.

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Section: Non-markovian Characteristics Of Dynamic Graphsmentioning

confidence: 99%

De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs

Qarkaxhija¹,

Perri²,

Scholtes³

2022

Preprint

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“…Current works primarily focus on graphs which can model only pairwise relations in data. Emerging research has shown that higher-order relations that involve more than two entities often reveal more significant information in many applications [7][8][9][10][11]. For example, higher-order network motifs build the fundamental blocks of many real-world networks [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Equivariant Hypergraph Diffusion Neural Operators

Peihao¹,

Yang²,

Liu³

et al. 2022

Preprint

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Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higherorder relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably approximates any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN 1 uniformly outperforms the best baselines over these nine datasets and achieves more than 2%↑ in prediction accuracy over four datasets therein.

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“…Although an expanding body of research attests to the increased utility of hypergraphbased analyses, many network science methods have been historically developed explicitly (and often, exclusively) for graph-based analyses and do not directly translate to hypergraphs. Consequently, new framework are being developed for representation, learning and analysis of hypergraphs, see [2], [3] for a recent survey. These include techniques for converting hypergraphs into graphs and defining hypergraph Laplacian [7], higher-order random walks-based hypergraph analysis [8], and defining dynamics on hypergraphs [9].…”

Section: Introductionmentioning

confidence: 99%

Hypergraph Dissimilarity Measures

Surana,

Chen,

Rajapakse

2021

Preprint

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In this paper, we propose two novel approaches for hypergraph comparison. The first approach transforms the hypergraph into a graph representation for use of standard graph dissimilarity measures. The second approach exploits the mathematics of tensors to intrinsically capture multi-way relations. For each approach, we present measures that assess hypergraph dissimilarity at a specific scale or provide a more holistic multi-scale comparison. We test these measures on synthetic hypergraphs and apply them to biological datasets.

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Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data

Cited by 5 publications

References 30 publications

De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs

De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs

Equivariant Hypergraph Diffusion Neural Operators

Hypergraph Dissimilarity Measures

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