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Spectral partitioning in equitable graphs

Overview of attention for article published in arXiv, June 2017
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (81st percentile)
  • High Attention Score compared to outputs of the same age and source (93rd percentile)

Mentioned by

twitter
18 tweeters

Readers on

mendeley
3 Mendeley
Title
Spectral partitioning in equitable graphs
Published in
arXiv, June 2017
DOI 10.1103/physreve.95.062310
Pubmed ID
Authors

Paolo Barucca

Abstract

Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.

Twitter Demographics

The data shown below were collected from the profiles of 18 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 3 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 3 100%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 2 67%
Researcher 1 33%
Readers by discipline Count As %
Mathematics 2 67%
Physics and Astronomy 1 33%

Attention Score in Context

This research output has an Altmetric Attention Score of 9. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 22 March 2018.
All research outputs
#1,617,947
of 12,365,836 outputs
Outputs from arXiv
#31,376
of 551,371 outputs
Outputs of similar age
#49,029
of 268,138 outputs
Outputs of similar age from arXiv
#1,510
of 23,497 outputs
Altmetric has tracked 12,365,836 research outputs across all sources so far. Compared to these this one has done well and is in the 86th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 551,371 research outputs from this source. They receive a mean Attention Score of 3.3. This one has done particularly well, scoring higher than 94% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 268,138 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 81% of its contemporaries.
We're also able to compare this research output to 23,497 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 93% of its contemporaries.