Provable and Practical Approximations for the Degree Distribution using Sublinear Graph Samples

Eden, Talya; Jain, Shweta; Pınar, Ali; Ron, Dana; Seshadhri, C.

doi:10.1145/3178876.3186111

Cited by 31 publications

(15 citation statements)

References 34 publications

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“…Fast calculation of clustering coefficient and many other properties by sampling are proposed in [13,16]. Provable approximation approach for degree distribution using sublinear graph samples is further discussed in [12].…”

Section: Social Network Sampling Techniquesmentioning

confidence: 99%

Sake

Lin

Song

et al. 2021

ACM Trans. Knowl. Discov. Data

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Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE , a <underline>S</underline> ampling-based <underline>A</underline> lgorithm for fast <underline>K</underline> atz centrality <underline>E</underline> stimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.

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Section: Social Network Sampling Techniquesmentioning

confidence: 99%

Sake

Lin

Song

et al. 2021

ACM Trans. Knowl. Discov. Data

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“…Moreover, the presence of even a small number of high degree nodes can lead to over-smoothing [28,26,35] of node features for deep GNNs. To counter such effects a number of unsupervised approaches for graph sparsification [4,5,1,7,33,20,23] as well as recent supervised approaches like DropEdge [28] and NeuralSparse [41] have been proposed. Given an input graph, the unsupervised methods extract a representative subgraph while preserving the original graph's crucial properties like its spectral properties, node-degree and distance distribution, and clustering.…”

Section: Related Workmentioning

confidence: 99%

Learnt Sparsification for Interpretable Graph Neural Networks

Rathee¹,

Zhang²,

Funke³

et al. 2021

Preprint

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Graph neural networks (GNNs) have achieved great success on various tasks and fields that require relational modeling. GNNs aggregate node features using the graph structure as inductive biases resulting in flexible and powerful models. However, GNNs remain hard to interpret as the interplay between node features and graph structure is only implicitly learned. In this paper, we propose a novel method called KEdge for explicitly sparsifying the underlying graph by removing unnecessary neighbors. Our key idea is based on a tractable method for sparsification using the Hard Kumaraswamy distribution that can be used in conjugation with any GNN model. KEdge learns edge masks in a modular fashion trained with any GNN allowing for gradient-based optimization in an end-to-end fashion. We demonstrate through extensive experiments that our model KEdge can prune a large proportion of the edges with only a minor effect on the test accuracy. Specifically, in the PubMed dataset, KEdge learns to drop more than 80% of the edges with an accuracy drop of merely ≈ 2% showing that graph structure has only a small contribution in comparison to node features. Finally, we also show that KEdge effectively counters the over-smoothing phenomena in deep GNNs by maintaining good task performance with increasing GNN layers.

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“…Graph sparsification aims to approximate a given graph by a graph with fewer edges for efficient computation. Depending on final goals, there are cut-sparsifiers [17], pair-wise distance preserving sparsifiers [18] and spectral sparsifiers [19,20] , among others [21,22,23,24]. In this work, we use spectral sparsification to choose a randomized subgraph.…”

Section: Related Workmentioning

confidence: 99%

Fast Graph Attention Networks Using Effective Resistance Based Graph Sparsification

Srinivasa,

Xiao,

Glass

et al. 2020

Preprint

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The attention mechanism has demonstrated superior performance for inference over nodes in graph neural networks (GNNs), however, they result in a high computational burden during both training and inference. We propose FastGAT, a method to make attention based GNNs lightweight by using spectral sparsification to generate an optimal pruning of the input graph. This results in a per-epoch time that is almost linear in the number of graph nodes as opposed to quadratic. Further, we provide a re-formulation of a specific attention based GNN, Graph Attention Network (GAT) that interprets it as a graph convolution method using the random walk normalized graph Laplacian. Using this framework, we theoretically prove that spectral sparsification preserves the features computed by the GAT model, thereby justifying our FastGAT algorithm. We experimentally evaluate FastGAT on several large real world graph datasets for node classification tasks, FastGAT can dramatically reduce (up to 10x) the computational time and memory requirements, allowing the usage of attention based GNNs on large graphs.

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Provable and Practical Approximations for the Degree Distribution using Sublinear Graph Samples

Cited by 31 publications

References 34 publications

Sake

Sake

Learnt Sparsification for Interpretable Graph Neural Networks

Fast Graph Attention Networks Using Effective Resistance Based Graph Sparsification

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