Analyzing modularity maximization in approximation, heuristic, and graph neural network algorithms for community detection Article Swipe
Samin Aref
,
Mahdi Mostajabdaveh
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.jocs.2024.102283
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.jocs.2024.102283
Community detection, which involves partitioning nodes within a network, has widespread applications across computational sciences. Modularity-based algorithms identify communities by attempting to maximize the modularity function across network node partitions. Our study assesses the performance of various modularity-based algorithms in obtaining optimal partitions. Our analysis utilizes 104 networks, including both real-world instances from diverse contexts and modular graphs from two families of synthetic benchmarks. We analyze ten inexact modularity-based algorithms against the exact integer programming baseline that globally optimizes modularity. Our comparative analysis includes eight heuristics, two variants of a graph neural network algorithm, and nine variations of the Bayan approximation algorithm. Our findings reveal that the average modularity-based heuristic yields optimal partitions in only 43.9% of the 104 networks analyzed. Graph neural networks and approximate Bayan, on average, achieve optimality on 68.7% and 82.3% of the networks respectively. Additionally, our analysis of three partition similarity metrics exposes substantial dissimilarities between high-modularity sub-optimal partitions and any optimal partition of the networks. We observe that near-optimal partitions are often disproportionately dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of the commonly used modularity-based methods: they rarely produce an optimal partition or a partition resembling an optimal partition even on networks with modular structures. If modularity is to be used for detecting communities, we recommend approximate optimization algorithms for a methodologically sound usage of modularity within its applicability limits. This article is an extended version of an ICCS 2023 conference paper (Aref et al., 2023).
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.jocs.2024.102283
- OA Status
- hybrid
- Cited By
- 16
- References
- 75
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4394566534
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4394566534Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1016/j.jocs.2024.102283Digital Object Identifier
- Title
-
Analyzing modularity maximization in approximation, heuristic, and graph neural network algorithms for community detectionWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-04-08Full publication date if available
- Authors
-
Samin Aref, Mahdi MostajabdavehList of authors in order
- Landing page
-
https://doi.org/10.1016/j.jocs.2024.102283Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.jocs.2024.102283Direct OA link when available
- Concepts
-
Modularity (biology), Heuristic, Computer science, Maximization, Artificial neural network, Graph, Algorithm, Theoretical computer science, Artificial intelligence, Mathematical optimization, Mathematics, Genetics, BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
16Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 10, 2024: 5, 2023: 1Per-year citation counts (last 5 years)
- References (count)
-
75Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4394566534 |
|---|---|
| doi | https://doi.org/10.1016/j.jocs.2024.102283 |
| ids.doi | https://doi.org/10.1016/j.jocs.2024.102283 |
| ids.openalex | https://openalex.org/W4394566534 |
| fwci | 8.13503119 |
| type | article |
| title | Analyzing modularity maximization in approximation, heuristic, and graph neural network algorithms for community detection |
| biblio.issue | |
| biblio.volume | 78 |
| biblio.last_page | 102283 |
| biblio.first_page | 102283 |
| topics[0].id | https://openalex.org/T10064 |
| topics[0].field.id | https://openalex.org/fields/31 |
| topics[0].field.display_name | Physics and Astronomy |
| topics[0].score | 1.0 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/3109 |
| topics[0].subfield.display_name | Statistical and Nonlinear Physics |
| topics[0].display_name | Complex Network Analysis Techniques |
| topics[1].id | https://openalex.org/T10637 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9904999732971191 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1702 |
| topics[1].subfield.display_name | Artificial Intelligence |
| topics[1].display_name | Advanced Clustering Algorithms Research |
| topics[2].id | https://openalex.org/T11273 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9865000247955322 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1702 |
| topics[2].subfield.display_name | Artificial Intelligence |
| topics[2].display_name | Advanced Graph Neural Networks |
| is_xpac | False |
| apc_list.value | 2810 |
| apc_list.currency | USD |
| apc_list.value_usd | 2810 |
| apc_paid.value | 2810 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 2810 |
| concepts[0].id | https://openalex.org/C2779478453 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7273169755935669 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q6889748 |
| concepts[0].display_name | Modularity (biology) |
| concepts[1].id | https://openalex.org/C173801870 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6335645914077759 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q201413 |
| concepts[1].display_name | Heuristic |
| concepts[2].id | https://openalex.org/C41008148 |
| concepts[2].level | 0 |
| concepts[2].score | 0.6279904246330261 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[2].display_name | Computer science |
| concepts[3].id | https://openalex.org/C2776330181 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5918259620666504 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q18358244 |
| concepts[3].display_name | Maximization |
| concepts[4].id | https://openalex.org/C50644808 |
| concepts[4].level | 2 |
| concepts[4].score | 0.44726625084877014 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q192776 |
| concepts[4].display_name | Artificial neural network |
| concepts[5].id | https://openalex.org/C132525143 |
| concepts[5].level | 2 |
| concepts[5].score | 0.4296448230743408 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q141488 |
| concepts[5].display_name | Graph |
| concepts[6].id | https://openalex.org/C11413529 |
| concepts[6].level | 1 |
| concepts[6].score | 0.4087708294391632 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[6].display_name | Algorithm |
| concepts[7].id | https://openalex.org/C80444323 |
| concepts[7].level | 1 |
| concepts[7].score | 0.37932834029197693 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q2878974 |
| concepts[7].display_name | Theoretical computer science |
| concepts[8].id | https://openalex.org/C154945302 |
| concepts[8].level | 1 |
| concepts[8].score | 0.3781646192073822 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[8].display_name | Artificial intelligence |
| concepts[9].id | https://openalex.org/C126255220 |
| concepts[9].level | 1 |
| concepts[9].score | 0.2809000611305237 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[9].display_name | Mathematical optimization |
| concepts[10].id | https://openalex.org/C33923547 |
| concepts[10].level | 0 |
| concepts[10].score | 0.23798075318336487 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[10].display_name | Mathematics |
| concepts[11].id | https://openalex.org/C54355233 |
| concepts[11].level | 1 |
| concepts[11].score | 0.0 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q7162 |
| concepts[11].display_name | Genetics |
| concepts[12].id | https://openalex.org/C86803240 |
| concepts[12].level | 0 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[12].display_name | Biology |
| keywords[0].id | https://openalex.org/keywords/modularity |
| keywords[0].score | 0.7273169755935669 |
| keywords[0].display_name | Modularity (biology) |
| keywords[1].id | https://openalex.org/keywords/heuristic |
| keywords[1].score | 0.6335645914077759 |
| keywords[1].display_name | Heuristic |
| keywords[2].id | https://openalex.org/keywords/computer-science |
| keywords[2].score | 0.6279904246330261 |
| keywords[2].display_name | Computer science |
| keywords[3].id | https://openalex.org/keywords/maximization |
| keywords[3].score | 0.5918259620666504 |
| keywords[3].display_name | Maximization |
| keywords[4].id | https://openalex.org/keywords/artificial-neural-network |
| keywords[4].score | 0.44726625084877014 |
| keywords[4].display_name | Artificial neural network |
| keywords[5].id | https://openalex.org/keywords/graph |
| keywords[5].score | 0.4296448230743408 |
| keywords[5].display_name | Graph |
| keywords[6].id | https://openalex.org/keywords/algorithm |
| keywords[6].score | 0.4087708294391632 |
| keywords[6].display_name | Algorithm |
| keywords[7].id | https://openalex.org/keywords/theoretical-computer-science |
| keywords[7].score | 0.37932834029197693 |
| keywords[7].display_name | Theoretical computer science |
| keywords[8].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[8].score | 0.3781646192073822 |
| keywords[8].display_name | Artificial intelligence |
| keywords[9].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[9].score | 0.2809000611305237 |
| keywords[9].display_name | Mathematical optimization |
| keywords[10].id | https://openalex.org/keywords/mathematics |
| keywords[10].score | 0.23798075318336487 |
| keywords[10].display_name | Mathematics |
| language | en |
| locations[0].id | doi:10.1016/j.jocs.2024.102283 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S192071280 |
| locations[0].source.issn | 1877-7503, 1877-7511 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 1877-7503 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Journal of Computational Science |
| locations[0].source.host_organization | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_name | Elsevier BV |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_lineage_names | Elsevier BV |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Journal of Computational Science |
| locations[0].landing_page_url | https://doi.org/10.1016/j.jocs.2024.102283 |
| locations[1].id | pmh:oai:publications.polymtl.ca:58198 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401013 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PolyPublie (École Polytechnique de Montréal) |
| locations[1].source.host_organization | https://openalex.org/I45683168 |
| locations[1].source.host_organization_name | Polytechnique Montréal |
| locations[1].source.host_organization_lineage | https://openalex.org/I45683168 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | acceptedVersion |
| locations[1].raw_type | Article de revue |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | False |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | |
| locations[2].id | pmh:oai:publications.polymtl.ca:58482 |
| locations[2].is_oa | False |
| locations[2].source.id | https://openalex.org/S4306401013 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | PolyPublie (École Polytechnique de Montréal) |
| locations[2].source.host_organization | https://openalex.org/I45683168 |
| locations[2].source.host_organization_name | Polytechnique Montréal |
| locations[2].source.host_organization_lineage | https://openalex.org/I45683168 |
| locations[2].license | |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | Article de revue |
| locations[2].license_id | |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | https://publications.polymtl.ca/58482/ |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5067809445 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-5870-9253 |
| authorships[0].author.display_name | Samin Aref |
| authorships[0].countries | CA |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I185261750 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mechanical and Industrial Engineering, University of Toronto, M5S3G8, Canada |
| authorships[0].institutions[0].id | https://openalex.org/I185261750 |
| authorships[0].institutions[0].ror | https://ror.org/03dbr7087 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I185261750 |
| authorships[0].institutions[0].country_code | CA |
| authorships[0].institutions[0].display_name | University of Toronto |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Samin Aref |
| authorships[0].is_corresponding | True |
| authorships[0].raw_affiliation_strings | Department of Mechanical and Industrial Engineering, University of Toronto, M5S3G8, Canada |
| authorships[1].author.id | https://openalex.org/A5042614566 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-2816-909X |
| authorships[1].author.display_name | Mahdi Mostajabdaveh |
| authorships[1].countries | CA |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I45683168 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Mathematical and Industrial Engineering, Polytechnique Montreal, H3T1J4, Canada |
| authorships[1].institutions[0].id | https://openalex.org/I45683168 |
| authorships[1].institutions[0].ror | https://ror.org/05f8d4e86 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I45683168 |
| authorships[1].institutions[0].country_code | CA |
| authorships[1].institutions[0].display_name | Polytechnique Montréal |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Mahdi Mostajabdaveh |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Mathematical and Industrial Engineering, Polytechnique Montreal, H3T1J4, Canada |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1016/j.jocs.2024.102283 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Analyzing modularity maximization in approximation, heuristic, and graph neural network algorithms for community detection |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10064 |
| primary_topic.field.id | https://openalex.org/fields/31 |
| primary_topic.field.display_name | Physics and Astronomy |
| primary_topic.score | 1.0 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/3109 |
| primary_topic.subfield.display_name | Statistical and Nonlinear Physics |
| primary_topic.display_name | Complex Network Analysis Techniques |
| related_works | https://openalex.org/W4230687177, https://openalex.org/W1968829728, https://openalex.org/W2349859869, https://openalex.org/W3120118008, https://openalex.org/W4316651471, https://openalex.org/W2051365847, https://openalex.org/W2367249529, https://openalex.org/W2027187261, https://openalex.org/W2088885441, https://openalex.org/W1943342825 |
| cited_by_count | 16 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 10 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 5 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 1 |
| locations_count | 3 |
| best_oa_location.id | doi:10.1016/j.jocs.2024.102283 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S192071280 |
| best_oa_location.source.issn | 1877-7503, 1877-7511 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 1877-7503 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Journal of Computational Science |
| best_oa_location.source.host_organization | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_name | Elsevier BV |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_lineage_names | Elsevier BV |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Journal of Computational Science |
| best_oa_location.landing_page_url | https://doi.org/10.1016/j.jocs.2024.102283 |
| primary_location.id | doi:10.1016/j.jocs.2024.102283 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S192071280 |
| primary_location.source.issn | 1877-7503, 1877-7511 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1877-7503 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Journal of Computational Science |
| primary_location.source.host_organization | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_name | Elsevier BV |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_lineage_names | Elsevier BV |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Journal of Computational Science |
| primary_location.landing_page_url | https://doi.org/10.1016/j.jocs.2024.102283 |
| publication_date | 2024-04-08 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W2550720082, https://openalex.org/W4288704342, https://openalex.org/W2151936673, https://openalex.org/W6788928114, https://openalex.org/W2416738288, https://openalex.org/W2950283584, https://openalex.org/W2963890422, https://openalex.org/W2951271819, https://openalex.org/W2111642621, https://openalex.org/W2127048411, https://openalex.org/W6843478659, https://openalex.org/W2128366083, https://openalex.org/W2069543694, https://openalex.org/W2766665124, https://openalex.org/W2119998616, https://openalex.org/W2169148563, https://openalex.org/W6793955985, https://openalex.org/W2168346701, https://openalex.org/W2164998314, https://openalex.org/W2104240253, https://openalex.org/W2098236822, https://openalex.org/W2731024717, https://openalex.org/W3168952105, https://openalex.org/W2137385671, https://openalex.org/W2061099285, https://openalex.org/W4294688230, https://openalex.org/W2047940964, https://openalex.org/W2131681506, https://openalex.org/W2025543856, https://openalex.org/W2063251739, https://openalex.org/W2156028561, https://openalex.org/W2897249806, https://openalex.org/W2949078036, https://openalex.org/W2161455936, https://openalex.org/W2047766788, https://openalex.org/W2966321063, https://openalex.org/W2109726592, https://openalex.org/W2057504236, https://openalex.org/W6684050148, https://openalex.org/W2965757567, https://openalex.org/W4318940499, https://openalex.org/W4220964149, https://openalex.org/W2792105640, https://openalex.org/W2949635546, https://openalex.org/W6850525149, https://openalex.org/W2023655578, https://openalex.org/W3004293141, https://openalex.org/W2622574927, https://openalex.org/W6691142915, https://openalex.org/W2095189226, https://openalex.org/W2749914992, https://openalex.org/W2898992240, https://openalex.org/W3102247132, https://openalex.org/W2970350994, https://openalex.org/W6781504184, https://openalex.org/W2024996305, https://openalex.org/W3113097209, https://openalex.org/W2045387243, https://openalex.org/W4306725833, https://openalex.org/W4383468713, https://openalex.org/W3126033509, https://openalex.org/W4295695453, https://openalex.org/W4212774754, https://openalex.org/W3155044266, https://openalex.org/W3102641634, https://openalex.org/W2162833336, https://openalex.org/W4394186913, https://openalex.org/W3102747296, https://openalex.org/W3128381039, https://openalex.org/W2184148260, https://openalex.org/W4382703215, https://openalex.org/W3125316886, https://openalex.org/W3099768174, https://openalex.org/W3106188259, https://openalex.org/W3047166675 |
| referenced_works_count | 75 |
| abstract_inverted_index.a | 8, 90, 181, 197, 224 |
| abstract_inverted_index.If | 209 |
| abstract_inverted_index.We | 65, 162 |
| abstract_inverted_index.an | 193, 200, 237, 241 |
| abstract_inverted_index.be | 213 |
| abstract_inverted_index.by | 20 |
| abstract_inverted_index.et | 247 |
| abstract_inverted_index.in | 40, 114 |
| abstract_inverted_index.is | 211, 236 |
| abstract_inverted_index.of | 36, 62, 89, 98, 117, 136, 143, 159, 184, 228, 240 |
| abstract_inverted_index.on | 128, 132, 204 |
| abstract_inverted_index.or | 196 |
| abstract_inverted_index.to | 22, 171, 180, 212 |
| abstract_inverted_index.we | 218 |
| abstract_inverted_index.104 | 47, 119 |
| abstract_inverted_index.Our | 31, 44, 81, 103 |
| abstract_inverted_index.and | 56, 95, 125, 134, 155 |
| abstract_inverted_index.any | 156, 172 |
| abstract_inverted_index.are | 167 |
| abstract_inverted_index.for | 215, 223 |
| abstract_inverted_index.has | 10 |
| abstract_inverted_index.its | 231 |
| abstract_inverted_index.our | 141, 177 |
| abstract_inverted_index.ten | 67 |
| abstract_inverted_index.the | 24, 34, 72, 99, 107, 118, 137, 160, 185 |
| abstract_inverted_index.two | 60, 87 |
| abstract_inverted_index.2023 | 243 |
| abstract_inverted_index.ICCS | 242 |
| abstract_inverted_index.This | 234 |
| abstract_inverted_index.al., | 248 |
| abstract_inverted_index.both | 50 |
| abstract_inverted_index.even | 203 |
| abstract_inverted_index.from | 53, 59 |
| abstract_inverted_index.nine | 96 |
| abstract_inverted_index.node | 29 |
| abstract_inverted_index.only | 115 |
| abstract_inverted_index.that | 77, 106, 164 |
| abstract_inverted_index.they | 190 |
| abstract_inverted_index.used | 187, 214 |
| abstract_inverted_index.with | 206 |
| abstract_inverted_index.(Aref | 246 |
| abstract_inverted_index.43.9% | 116 |
| abstract_inverted_index.68.7% | 133 |
| abstract_inverted_index.82.3% | 135 |
| abstract_inverted_index.Bayan | 100 |
| abstract_inverted_index.Graph | 122 |
| abstract_inverted_index.Taken | 175 |
| abstract_inverted_index.eight | 85 |
| abstract_inverted_index.exact | 73 |
| abstract_inverted_index.graph | 91 |
| abstract_inverted_index.nodes | 6 |
| abstract_inverted_index.often | 168 |
| abstract_inverted_index.paper | 245 |
| abstract_inverted_index.sound | 226 |
| abstract_inverted_index.study | 32 |
| abstract_inverted_index.three | 144 |
| abstract_inverted_index.usage | 227 |
| abstract_inverted_index.which | 3 |
| abstract_inverted_index.2023). | 249 |
| abstract_inverted_index.Bayan, | 127 |
| abstract_inverted_index.across | 13, 27 |
| abstract_inverted_index.graphs | 58 |
| abstract_inverted_index.neural | 92, 123 |
| abstract_inverted_index.points | 179 |
| abstract_inverted_index.rarely | 191 |
| abstract_inverted_index.reveal | 105 |
| abstract_inverted_index.within | 7, 230 |
| abstract_inverted_index.yields | 111 |
| abstract_inverted_index.achieve | 130 |
| abstract_inverted_index.against | 71 |
| abstract_inverted_index.analyze | 66 |
| abstract_inverted_index.article | 235 |
| abstract_inverted_index.average | 108 |
| abstract_inverted_index.between | 151 |
| abstract_inverted_index.crucial | 182 |
| abstract_inverted_index.diverse | 54 |
| abstract_inverted_index.exposes | 148 |
| abstract_inverted_index.inexact | 68 |
| abstract_inverted_index.integer | 74 |
| abstract_inverted_index.limits. | 233 |
| abstract_inverted_index.metrics | 147 |
| abstract_inverted_index.modular | 57, 207 |
| abstract_inverted_index.network | 28, 93 |
| abstract_inverted_index.observe | 163 |
| abstract_inverted_index.optimal | 42, 112, 157, 173, 194, 201 |
| abstract_inverted_index.produce | 192 |
| abstract_inverted_index.various | 37 |
| abstract_inverted_index.version | 239 |
| abstract_inverted_index.analysis | 45, 83, 142, 178 |
| abstract_inverted_index.assesses | 33 |
| abstract_inverted_index.average, | 129 |
| abstract_inverted_index.baseline | 76 |
| abstract_inverted_index.commonly | 186 |
| abstract_inverted_index.contexts | 55 |
| abstract_inverted_index.extended | 238 |
| abstract_inverted_index.families | 61 |
| abstract_inverted_index.findings | 104 |
| abstract_inverted_index.function | 26 |
| abstract_inverted_index.globally | 78 |
| abstract_inverted_index.identify | 18 |
| abstract_inverted_index.includes | 84 |
| abstract_inverted_index.involves | 4 |
| abstract_inverted_index.maximize | 23 |
| abstract_inverted_index.methods: | 189 |
| abstract_inverted_index.network, | 9 |
| abstract_inverted_index.networks | 120, 124, 138, 205 |
| abstract_inverted_index.utilizes | 46 |
| abstract_inverted_index.variants | 88 |
| abstract_inverted_index.ABSTRACT: | 0 |
| abstract_inverted_index.Community | 1 |
| abstract_inverted_index.analyzed. | 121 |
| abstract_inverted_index.detecting | 216 |
| abstract_inverted_index.heuristic | 110 |
| abstract_inverted_index.including | 49 |
| abstract_inverted_index.instances | 52 |
| abstract_inverted_index.networks, | 48 |
| abstract_inverted_index.networks. | 161 |
| abstract_inverted_index.obtaining | 41 |
| abstract_inverted_index.optimizes | 79 |
| abstract_inverted_index.partition | 145, 158, 195, 198, 202 |
| abstract_inverted_index.recommend | 219 |
| abstract_inverted_index.sciences. | 15 |
| abstract_inverted_index.synthetic | 63 |
| abstract_inverted_index.together, | 176 |
| abstract_inverted_index.algorithm, | 94 |
| abstract_inverted_index.algorithm. | 102 |
| abstract_inverted_index.algorithms | 17, 39, 70, 222 |
| abstract_inverted_index.attempting | 21 |
| abstract_inverted_index.conference | 244 |
| abstract_inverted_index.detection, | 2 |
| abstract_inverted_index.dissimilar | 170 |
| abstract_inverted_index.limitation | 183 |
| abstract_inverted_index.modularity | 25, 210, 229 |
| abstract_inverted_index.optimality | 131 |
| abstract_inverted_index.partition. | 174 |
| abstract_inverted_index.partitions | 113, 154, 166 |
| abstract_inverted_index.real-world | 51 |
| abstract_inverted_index.resembling | 199 |
| abstract_inverted_index.similarity | 146 |
| abstract_inverted_index.variations | 97 |
| abstract_inverted_index.widespread | 11 |
| abstract_inverted_index.approximate | 126, 220 |
| abstract_inverted_index.benchmarks. | 64 |
| abstract_inverted_index.communities | 19 |
| abstract_inverted_index.comparative | 82 |
| abstract_inverted_index.heuristics, | 86 |
| abstract_inverted_index.modularity. | 80 |
| abstract_inverted_index.partitions. | 30, 43 |
| abstract_inverted_index.performance | 35 |
| abstract_inverted_index.programming | 75 |
| abstract_inverted_index.structures. | 208 |
| abstract_inverted_index.sub-optimal | 153 |
| abstract_inverted_index.substantial | 149 |
| abstract_inverted_index.applications | 12 |
| abstract_inverted_index.communities, | 217 |
| abstract_inverted_index.near-optimal | 165 |
| abstract_inverted_index.optimization | 221 |
| abstract_inverted_index.partitioning | 5 |
| abstract_inverted_index.Additionally, | 140 |
| abstract_inverted_index.applicability | 232 |
| abstract_inverted_index.approximation | 101 |
| abstract_inverted_index.computational | 14 |
| abstract_inverted_index.respectively. | 139 |
| abstract_inverted_index.dissimilarities | 150 |
| abstract_inverted_index.high-modularity | 152 |
| abstract_inverted_index.Modularity-based | 16 |
| abstract_inverted_index.methodologically | 225 |
| abstract_inverted_index.modularity-based | 38, 69, 109, 188 |
| abstract_inverted_index.disproportionately | 169 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 89 |
| corresponding_author_ids | https://openalex.org/A5067809445 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I185261750 |
| citation_normalized_percentile.value | 0.96486238 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |