Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

Liu, Tony; Firoz, Jesun Sahariar; Lumsdaine, Andrew; Joslyn, Cliff; Aksoy, Sinan; Praggastis, Brenda; Gebremedhin, Assefaw H.

doi:10.1109/hipc53243.2021.00045

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…To further demonstrate Observation 2, we construct the sline graph [22] of a hypergraph by abstracting hyperedges as new vertices and creating new edges for representing specified overlap relationships where the common vertex count is greater than or equal to s. The s-line graph retains the critical topological structure features of the original hypergraph while removing unimportant overlap relationships. Fig.…”

Section: Overcoming Inefficienciesmentioning

confidence: 99%

PhGraph: A High-Performance ReRAM-Based Accelerator for Hypergraph Applications

Zheng,

Hu,

Wang

et al. 2024

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Section: Overcoming Inefficienciesmentioning

confidence: 99%

PhGraph: A High-Performance ReRAM-Based Accelerator for Hypergraph Applications

Zheng,

Hu,

Wang

et al. 2024

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…Let

be the hypergraph, then

and

. According to the definition of the

-overlap, it is obvious that 1-overlap

exists between three sets of incident hyperedge pairs (i.e.,

, and

; the pair of hyperedges

and

also satisfy 2-overlap

; only one set of hyperedges

has 3-overlap

.The

-line graph [ 28 ]

of hypergraph

is a ordinary graph with vertex set

. For any

order line graph, two nodes

and

are adjacent if and only if condition

holds in hypergraph

, where

is the maximum number of shared nodes among hyperedges.…”

Section: Preliminariesmentioning

confidence: 99%

“…, e 4 }. According to the definition of the s-overlap, it is obvious that 1-overlap (s = 1) exists between three sets of incident hyperedge pairs (i.e., (e 1 , e 2 ), (e 2 , e 3 ), and (e 2 , e 4 )); the pair of hyperedges (e 1 , e 2 ) and (e 2 , e 3 ) also satisfy 2-overlap (s = 2); only one set of hyperedges (e 2 , e 3 ) has 3-overlap (s = 3).The s-line graph [28] L s (H) of hypergraph H is a ordinary graph with vertex set V s = E. For any s = 1, 2, . .…”

Section: Hypergraph and S-line Graphmentioning

confidence: 99%

Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy

Hu,

Tian,

Zhang

2023

Entropy

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Hypergraphs have become an accurate and natural expression of high-order coupling relationships in complex systems. However, applying high-order information from networks to vital node identification tasks still poses significant challenges. This paper proposes a von Neumann entropy-based hypergraph vital node identification method (HVC) that integrates high-order information as well as its optimized version (semi-SAVC). HVC is based on the high-order line graph structure of hypergraphs and measures changes in network complexity using von Neumann entropy. It integrates s-line graph information to quantify node importance in the hypergraph by mapping hyperedges to nodes. In contrast, semi-SAVC uses a quadratic approximation of von Neumann entropy to measure network complexity and considers only half of the maximum order of the hypergraph’s s-line graph to balance accuracy and efficiency. Compared to the baseline methods of hyperdegree centrality, closeness centrality, vector centrality, and sub-hypergraph centrality, the new methods demonstrated superior identification of vital nodes that promote the maximum influence and maintain network connectivity in empirical hypergraph data, considering the influence and robustness factors. The correlation and monotonicity of the identification results were quantitatively analyzed and comprehensive experimental results demonstrate the superiority of the new methods. At the same time, a key non-trivial phenomenon was discovered: influence does not increase linearly as the s-line graph orders increase. We call this the saturation effect of high-order line graph information in hypergraph node identification. When the order reaches its saturation value, the addition of high-order information often acts as noise and affects propagation.

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High‐Order line graphs of fMRI data in major depressive disorder

Guo,

Huang,

Wang

et al. 2024

Medical Physics

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BackgroundResting‐state functional magnetic resonance imaging (rs‐fMRI) technology and the complex network theory can be used to elucidate the underlying mechanisms of brain diseases. The successful application of functional brain hypernetworks provides new perspectives for the diagnosis and evaluation of clinical brain diseases; however, many studies have not assessed the attribute information of hyperedges and could not retain the high‐order topology of hypergraphs. In addition, the study of multi‐scale and multi‐layered organizational properties of the human brain can provide richer and more accurate data features for classification models of depression.PurposeThis work aims to establish a more accurate classification framework for the diagnosis of major depressive disorder (MDD) using the high‐order line graph algorithm. And accuracy, sensitivity, specificity, precision, F1 score are used to validate its classification performance.MethodsBased on rs‐fMRI data from 38 MDD subjects and 28 controls, we constructed a human brain hypernetwork and introduced a line graph model, followed by the construction of a high‐order line graph model. The topological properties under each order line graph were calculated to measure the classification performance of the model. Finally, intergroup features that showed significant differences under each order line graph model were fused, and a support vector machine classifier was constructed using multi‐kernel learning. The Kolmogorov–Smirnov nonparametric permutation test was used as the feature selection method and the classification performance was measured with the leave‐one‐out cross‐validation method.ResultsThe high‐order line graph achieved a better classification performance compared with other traditional hypernetworks (accuracy = 92.42%, sensitivity = 92.86%, specificity = 92.11%, precision = 89.66%, F1 = 91.23%). Furthermore, the brain regions found in the present study have been previously shown to be associated with the pathology of depression.ConclusionsThis work validated the classification model based on the high‐order line graph, which can better express the topological features of the hypernetwork by comprehensively considering the hyperedge information under different connection strengths, thereby significantly improving the classification accuracy of MDD. Therefore, this method has potential for use in the clinical diagnosis of MDD.

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Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

Cited by 5 publications

References 23 publications

PhGraph: A High-Performance ReRAM-Based Accelerator for Hypergraph Applications

PhGraph: A High-Performance ReRAM-Based Accelerator for Hypergraph Applications

Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy

High‐Order line graphs of fMRI data in major depressive disorder

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