| Title |
Spectral partitioning in equitable graphs
|
|---|---|
| Published in |
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 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. |
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United Kingdom | 5 | 28% |
| United States | 3 | 17% |
| Italy | 1 | 6% |
| Japan | 1 | 6% |
| Belgium | 1 | 6% |
| Norway | 1 | 6% |
| Colombia | 1 | 6% |
| Unknown | 5 | 28% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 11 | 61% |
| Scientists | 6 | 33% |
| Unknown | 1 | 6% |
Mendeley readers
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 6 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 4 | 67% |
| Researcher | 1 | 17% |
| Student > Master | 1 | 17% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 2 | 33% |
| Physics and Astronomy | 2 | 33% |
| Business, Management and Accounting | 1 | 17% |
| Social Sciences | 1 | 17% |
Attention Score in Context
This research output has an Altmetric Attention Score of 10. 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 30 October 2020.
All research outputs
#3,636,209
of 25,477,125 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#988
of 21,035 outputs
Outputs of similar age
#62,909
of 327,706 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#22
of 409 outputs
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