Decompositions of triangle-dense graphs

Gupta, Rishi; Roughgarden, Tim; Seshadhri, C.

doi:10.1145/2554797.2554840

Cited by 10 publications

(1 citation statement)

References 37 publications

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“…The third algorithm is inspired by methods that build communities around pivot nodes. For instance, in a recent work by Gupta et al (2014), the authors prove that a social network can be decomposed into dense communities, which are balls of radius 2, centered on pivot vertices.…”

Section: Finding Dense Labeled Communitiesmentioning

confidence: 99%

Overlapping community detection in labeled graphs

Galbrun

Gionis

Tatti

2014

Data Min Knowl Disc

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We present a new approach for the problem of finding overlapping communities in graphs and social networks. Our approach consists of a novel problem definition and three accompanying algorithms. We are particularly interested in graphs that have labels on their vertices, although our methods are also applicable to graphs with no labels. Our goal is to find k communities so that the total edge density over all k communities is maximized. In the case of labeled graphs, we require that each community is succinctly described by a set of labels. This requirement provides a better understanding for the discovered communities. The proposed problem formulation leads to the discovery of vertex-overlapping and dense communities that cover as many graph edges as possible. We capture these properties with a simple objective function, which we solve by adapting efficient approximation algorithms for the generalized maximum-coverage problem and the densest-subgraph problem. Our proposed algorithm is a generic greedy scheme. We experiment with three variants of the scheme, obtained by varying the greedy step of finding a dense subgraph. We validate our algorithms by comparing with other state-of-the-art community-detection methods on a variety of performance measures. Our experiments confirm that our algorithms achieve results of high quality in terms of the reported measures, and are practical in terms of performance.

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Section: Finding Dense Labeled Communitiesmentioning

confidence: 99%

Overlapping community detection in labeled graphs

Galbrun

Gionis

Tatti

2014

Data Min Knowl Disc

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Quantum Architecture Search with Neural Predictor Based on Graph Measures

He,

Li,

Deng

et al. 2024

Adv Quantum Tech

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Quantum architecture search (QAS) has attracted increasing attention owing to its remarkable ability to automate the design of quantum circuits for variational quantum algorithms (VQAs). However, evaluating the performance of numerous quantum circuits is essential to provide feedback for the search strategy, which inevitably renders QAS computationally expensive. Performance predictors have emerged as highly efficient evaluation methods to mitigate this challenge. However, the performance predictor faces a critical challenge in reducing the required number of circuit‐performance pairs for training. This study encodes circuit architecture by representing a quantum circuit as a relational graph that emphasizes message exchange. Subsequently, valuable information about circuit architecture is extracted through three types of graph measures, including distance‐based, degree‐based, and cluster‐based measures. The graph measures define a smooth space related to circuit performance, facilitating the training of the performance predictor. The effectiveness of the proposed method is assessed across three tasks within variational quantum eigensolvers (VQE): identifying the ground states of the Transverse Field Ising Model (TFIM), the Heisenberg model, and the molecule. The simulation results demonstrate notable enhancements in predictive accuracy achieved by our method, coupled with a substantial reduction in the required number of training samples for the predictor.

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Testing for high‐dimensional geometry in random graphs

Bubeck

Ding

Eldan

et al. 2016

Random Struct Algorithms

113

236

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We study the problem of detecting the presence of an underlying high‐dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erdős‐Rényi random graph G(n, p). Under the alternative, the graph is generated from the G(n,p,d) model, where each vertex corresponds to a latent independent random vector uniformly distributed on the sphere double-struckSd−1, and two vertices are connected if the corresponding latent vectors are close enough. In the dense regime (i.e., p is a constant), we propose a near‐optimal and computationally efficient testing procedure based on a new quantity which we call signed triangles. The proof of the detection lower bound is based on a new bound on the total variation distance between a Wishart matrix and an appropriately normalized GOE matrix. In the sparse regime, we make a conjecture for the optimal detection boundary. We conclude the paper with some preliminary steps on the problem of estimating the dimension in G(n,p,d). © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 503–532, 2016

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Decompositions of triangle-dense graphs

Cited by 10 publications

References 37 publications

Overlapping community detection in labeled graphs

Overlapping community detection in labeled graphs

Quantum Architecture Search with Neural Predictor Based on Graph Measures

Testing for high‐dimensional geometry in random graphs

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