
Comparing largescale graphs based on quantum probability theory
In this paper, a new measurement to compare two largescale graphs based...
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GRASS: Spectral Sparsification Leveraging Scalable Spectral Perturbation Analysis
Spectral graph sparsification aims to find ultrasparse subgraphs whose ...
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GRASPEL: Graph Spectral Learning at Scale
Learning meaningful graphs from data plays important roles in many data ...
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PyTorchBigGraph: A Largescale Graph Embedding System
Graph embedding methods produce unsupervised node features from graphs t...
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Realtime IndexFree Single Source SimRank Processing on WebScale Graphs
Given a graph G and a node u in G, a single source SimRank query evaluat...
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Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications
The von Neumann graph entropy (VNGE) facilitates the measure of informat...
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SimilarityAware Spectral Sparsification by Edge Filtering
In recent years, spectral graph sparsification techniques that can compu...
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Just SLaQ When You Approximate: Accurate Spectral Distances for WebScale Graphs
Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis provides quintessential tools for studying the multiscale structure of graphs and is a wellsuited foundation for reasoning about differences between graphs. However, computing full spectrum of large graphs is computationally prohibitive; thus, spectral graph comparison methods often rely on rough approximation techniques with weak error guarantees. In this work, we propose SLaQ, an efficient and effective approximation technique for computing spectral distances between graphs with billions of nodes and edges. We derive the corresponding error bounds and demonstrate that accurate computation is possible in time linear in the number of graph edges. In a thorough experimental evaluation, we show that SLaQ outperforms existing methods, oftentimes by several orders of magnitude in approximation accuracy, and maintains comparable performance, allowing to compare millionscale graphs in a matter of minutes on a single machine.
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